Prof. Dr. Hans-Christoph Grunau

Prof. Dr. Hans-Christoph Grunau

Fakultät für Mathematik (FMA)
Institut für Analysis und Numerik (IAN)
Gebäude 03, Universitätsplatz 2, 39106, Magdeburg, G03-205
Start

Research Interests

  • Boundary value problems for Willmore surfaces
  • Qualitative properties of solutions of elliptic boundary value problems of higher order
  • Semilinear eigenvalue problems involving critical Sobolev exponents
  • Biharmonic equations with supercritical growth
  • Parabolic systems with critical growth
  • Navier-Stokes equations

 

 

Preiswerte Mathematik 

Ein Versuch, die sieben Milleniums-Preisaufgaben des Clay Mathematics Institute allgemein verständlich zu beschreiben.
Aktualisierte Version des Beitrags für das Magdeburger Wissenschaftsjournal 45-50, vol.1 (2004).

 


 

Was die Mathematik vom Wasser lernen kann 

Ein Versuch, die Grundidee der Variationsrechnung an einem konkreten Beispiel allgemein verständlich zu erläutern.
In gekürzter Form am 13. Oktober 2008 in der Wochenendbeilage der Magdeburger Volksstimme erschienen.

Seminar

Seminar

Organisers

Roger Bielawski (Hannover)
Hans-Christoph Grunau (Magdeburg)
Miles Simon (Magdeburg)
Knut Smoczyk (Hannover)

 



Thursday, November 28, 2019

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Gebäude 03, Raum 214

 

15.00-16.00 Massimiliano Morini (Parma):
Nonlinear stability results for nonlocal gradient flows
16.30-17.30 Ovidiu Munteanu (Storrs, Connecticut):
Green's function estimates and the Poisson equation

 

 


 

Previous sessions:

 


Thursday, July 4, 2019

Institut für Differentialgeometrie
Leibniz-Universtiät Hannover
Callinstr. 23, Seminarraum 016, Gebäude 3110

15.00-16.00

Tobias Weth (Frankfurt) :                                                                                                
Critical domains for the first nonzero Neumann eigenvalue in Riemannian manifolds

16.30-17.30

Boris Vertman (Oldenburg):
Perelman entropies on singular spaces

 


 

Thursday, May 9, 2019
Insitut für Analysis und Numerik
Otto-von-Guericke Universität Magdeburg
Universitätsplatz 2, Building 02, Room 111

15.00-16.00

Matteo Novaga (Università di Pisa):
Anisotropic and crystalline mean curvature flow

16.30-17.30

Alix Deruelle (Sorbonne Université Paris):
Classification of asymptotically conical 2D shrinking gradient Kähler-Ricci solitons

 


Thursday, January 24, 2019

Insitut für Differentialgeometrie
Leibniz-Universität Hannover
Callinstr. 23, Seminar Room 016, Building 3110

15.00-16.00

Andrea Mondino (Warwick, UK):
Some smooth applications of non-smooth Ricci curvature lower bounds

16.30-17.30

Uwe Semmelmann (Stuttgart):
The kernel of the Rarita-Schwinger operator on Riemannian spin manifolds

Thursday, July 5, 2018

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Callinstr. 23, Seminar Room 016, Building 3110

15.00-16.00 Fabrice Bethuel (Paris VI):
A counterexample to the weak density of smooth maps between manifolds in Sobolev spaces
16.30-17.30 Alexander Lytchak (Köln) :
Minimal discs in singular spaces

 


Thursday, April 26, 2018

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Aldo Pratelli (Erlangen):
On the closure of planar diffeomorphisms and non-crossing functions
16.30-17.30 Jiawei Liu (Magdeburg):
The conical Kähler-Ricci flow and related work

 


Thursday, January 25, 2018

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Callinstr. 23, Seminar Room 016, Building 3110

15.00-16.00 Heiko von der Mosel (Aachen):
Self-avoidance in higher dimensions - facts and open questions
16.30-17.30 Michael Singer (London):
Boundary-value problems for 4-dimensional HyperKaehler metrics

 


Thursday, December 7, 2017

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg,
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Fernando Galaz-Garcia (Karlsruhe):
Sufficiently collapsed Alexandrov 3-spaces
16.30-17.30 Thomas Schmidt (Hamburg):
Plateau's problem in infinite-dimensional spaces

 


Thursday, June 22, 2017

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Callinstr. 23, Seminar Room 016, Building 3110

15.00-16.00 Jason Lotay (UC London):
Laplacian flow in G_2-geometry 
16.30-17.30 Oliver Goertsches (Marburg):
On the basic Dolbeault cohomology of Sasakian manifolds  

 


Thursday, April 27, 2017

Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Friedrich Sauvigny (Cottbus):
Multiple solutions of the nonparametric Plateau problem in the Euclidean space R^p of   arbitrary dimension
16.30-17.30 Reto Buzano, born Müller (Queen Mary University of London):
The moduli space of two-convex embedded spheres and tori

 


Thursday, January 19, 2017

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.00-16.00 Hansjörg Geiges (Köln): Traps and plugs in symplectic dynamics  
16.30-17.30  Alberto Abbondandolo (Bochum)
On the length of shortest closed geodesics and shadows of symplectic balls  

 


Thursday, October 27, 2016

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 05, Room 307

15.00-16.00 Felix Schulze (University College London):
Ricci flow from spaces with isolated conical singularities
16.30-17.30 Felix Finster (Regensburg):
Lorentzian spectral geometry and the fermionic signature operator

 


Thursday, July 07, 2016 

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309 

15.00-16.00 Klaus Kröncke (Hamburg):
The moduli space of Ricci-flat metrics
16.30-17.30 Adriano Tomassini (Parma, Italy):
On the cohomology of complex and symplectic manifolds

 


Thursday, April 21, 2016 

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Tobias Lamm (Karlsruhe):
Conformal Willmore Tori
16.30-17.30 Heiner Olbermann (Bonn):
Symmetry breaking in indented elastic cones

 


Thursday, January 14, 2016

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Panagiotis Gianniotis (University College London, UK):
The size of the singular set of a Type I Ricci flow
16.30-17.30 Lisa Beck (Augsburg):
Duality, regularity and uniqueness for BV-minimizers

 


Thursday, November 05, 2015

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.00-16.00 Paul Bryan (Riemann Center for Geometry and Physics):
Harnack inequalities, Alexandrov reflection and ancient solutions of curvature flows on the sphere
16.30-17.30 Exotic nearly Kaehler structures on the 6-sphere and the product of two 3-spheres

 


Thursday, July 9, 2015

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Francisco Martin (Granada, Spain):
http://www-ian.math.uni-magdeburg.de/home/grunau/abstracts/F_Martin_2015.pdf
16.30-17.30 Andreas Gastel (Duisburg-Essen):
Minimizing polyharmonic maps

 


Thursday, January 29, 2015

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.00-16.00 Nicholas Alikakos (Athens, Greece):
A maximum principle for systems with variational structure
16.30-17.30 Towards a theory of pde's of mixed elliptic hyperbolic type

 


Thursday, November 27, 2014

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Anna Dall'Acqua (Ulm):
On the L^2-flow of elastic curves
16.30-17.30 Melanie Rupflin (Leipzig):
Global solutions and asymptotics of Teichmüller harmonic map flow

 


Thursday, July 10, 2014

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Sergey Grigorian (Edinburg, Texas, USA):
Flows of G2-structures
16.45-17.45 Peter Albers (Münster):
Orderability -- rigidity in contact geometry

 


Thursday, May 22, 2014

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Nikolai S. Nadirashvili (Aix-Marseille, z.Zt. Bielefeld):
Fully nonlinear elliptic equations and minimal cones
16.30-17.30 Guofang Wang (Freiburg):
Mass and geometric inequalities

 


Thursday, January 23, 2014

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Andrew Swann (Aarhus, Denmark):
Twists and special geometries
16.45-17.45 Karsten Grove (Notre Dame, USA):
Reflections in non-negative curvature

 


Thursday, November 14, 2013

Institut für Analysis und Numerik 
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Matthias Röger (Dortmund):
Minimization of bending energies under constraints
16.30-17.30 Mohameden Ould Ahmedou (Gießen):
Conformal metrics of prescribed Q-curvature on 4-manifolds

 


Thursday, July 11, 2013

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room B 302

15.15-16.15 Marcos Dajczer (IMPA, Rio de Janeiro):
Deformations preserving the Gauss map
16.45-17.45 Theodoros Vlachos (Ioannina, Greece):
The associated family of an elliptic surface and applications to minimal submanifolds

 


Thursday, April 18, 2013

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Christoph Böhm (Münster):
Ricci flow, Lie theory and sphere theorems
16.30-17.30 Herbert Koch (Bonn):
Parabolic differential equations with rough data

 


Thursday, January 31, 2013

Freie Universität Berlin
Fachbereich Mathematik und Informatik
Arnimallee 22 - Hörsaal B

14.00-15.00 Esther Cabezas Rivas (Münster):
A generalization of Gromov's almost flat manifold theorem
15.30-16.30 Tom Ilmanen (ETH Zürich):
Singularities of Mean Curvature Flow in R^3

 


Thursday, November 22, 2012

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Francisco Martin (Granada):
Gluing constructions for complete minimal surfaces with finite total curvature in H^2xR
16.45-17.45 Pieralberto Sicbaldi (Marseille):
New examples of extremal domains for the first eigenvalue of the Laplace-Beltrami operator

 


Thursday, June 28, 2012

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

16.00-17.00 Jan Metzger (Potsdam):
On isoperimetric surfaces in Riemannian manifolds
17.30-18.30 Emanuele Spadaro (MPI Leipzig):
Mean-convex sets and global barriers to minimal hypersurfaces

 


Thursday, April 26, 2012

Freie Universität Berlin
Fachbereich Mathematik und Informatik
Arnimallee 6, SR 032

14.00-15.00 Alexander Grigor'yan (Universität Bielefeld):
Negative eigenvalues of two-dimensional Schrödinger operators
15.30-16.30 Peter Topping (University of Warwick):
Mean curvature flow from cones

 


Thursday, January 26, 2012

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 106

15.00-16.00 Oliver Schnürer (Konstanz):
Gauß curvature flows of entire graphs
16.30-17.30 Peter Hornung (MPI Leipzig):
Analysis of intrinsically flat surfaces and the Willmore functional

 


Thursday, November 17, 2011

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Jost-Hinrich Eschenburg (Augsburg):
Symmetric spaces and division algebras
16.45-17.45 Andreas Savas-Halilaj (MPI Leipzig):
Bernstein type problems

 


Thursday, June 30, 2011

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Carlo Mantegazza (Scuola Normale Superiore di Pisa):
Flow by mean curvature inside a moving ambient space
16.30-17.30 Armin Schikorra (RWTH Aachen, z.Zt. ETH Zürich):
Regularity for fractional harmonic maps

 


Thursday, April 14, 2011

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Josef Dorfmeister (TU München):
Willmore spheres in Sn via loop groups
16.45-17.45 Peter Quast (Augsburg):
Centrioles in symmetric spaces

 


Thursday, January 27, 2011

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 05, Room 307

15.00-16.00 Olivier Druet (École normale supérieure de Lyon):
The notion of stability for elliptic PDEs
16.30-17.30 Simon Blatt (ETH Zürich):
The gradient flow of O'Hara's knot energies

 


Thursday, November 11, 2010

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Bernhard Hanke (Augsburg):
Homotopy groups of the moduli space of metrics of positive scalar curvature
16.45-17.45 Matthias Schneider (Heidelberg):
Closed magnetic geodesics

 


Thursday, July 1, 2010

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 106

14.45-15.45 Yann Bernard (Freiburg):
Local Palais-Smale sequences for the Willmore functional

16.30-17.30 Jan Metzger (Potsdam):
Small surfaces of Willmore type in Riemannian manifolds

 


Thursday, April 15, 2010

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Dmitri V. Alekseevsky (Edinburgh / Hamburg):
Subdistributions of the contact distribution, associated PDE of Monge-Ampere type and geometry of Lagrangian Grassmannian

16.45-17.45 Andreas Juhl (Humboldt-Universität Berlin / Uppsala):
The recursive structure of Q-curvature

 


Thursday, January 14, 2010

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 03, Room 214

15.00-16.00 Ben Schweizer (Dortmund):
Modelling porous media: degenerate equations and variational inequalities

16.15-17.15 Felix Schulze (FU Berlin):
Foliations of asymptotically flat manifolds by surfaces of Willmore type

 


Thursday, November 5, 2009

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Helga Baum (Humboldt-Universität Berlin):
A conformal analogon of Calabi Yau manifolds
16.45-17.45 Tilmann Wurzbacher (Metz):
Geometry and quantization of symplectic Howe pairs

 


Thursday, June 11, 2009

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 02, Room 111

15.15-16.15 Alberto Abbondandolo (Leipzig):
Estimates and computations in Rabinowitz-Floer homology
16.45-17.45 Matthias Schwarz (Leipzig):
Product structures in string topology and Floer homology

 


Thursday, April 16, 2009

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Lorenz Schwachhöfer (Dortmund):
Extrinsic symplectic symmetric spaces
16.45-17.45 Dorothee Schüth (Humboldt-Universität Berlin):
Spectral isolation of bi-invariant metrics on compact Lie groups

 


Thursday, January 8, 2009

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 02, Room 210

15.00-16.00 Michael Struwe (ETH Zürich):
The heat flow with a critical exponential nonlinearity
16.30-17.30 Sergio Conti (Bonn):
Multiscale decomposition of dislocation microstructures

 


Thursday, October 16, 2008

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 02, Room 210

15.15-16.15 Jiayu Li (ICTP Trieste, Italy):
Symplectic critical surfaces in Kähler surfaces
16.45-17.45 Matthias Röger (MPI Leipzig):
The Allen-Cahn action functional and its sharp interface limit

 


Thursday, June 12, 2008

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Vladimir Matveev (Jena):
Quadratic integrals of geodesic flows and solution of S. Lie problem
16.45-17.45 Klaus Mohnke (Humboldt-Universität Berlin):
Symplectic hypersurfaces and transversality in Gromov-Witten theory

 


Thursday, April 17, 2008

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Hans-Bert Rademacher (Leipzig):
Finsler metrics and closed geodesics
16.45-17.45 Wilderich Tuschmann (Kiel):
Almost nonnegative curvature

 


Thursday, January 17, 2008

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 05, Room 118

15.15-16.15 Reiner Schätzle (Tübingen):
Minimizers of the Willmore functional under fixed conformal class
16.45-17.45 Andrea Malchiodi (Sissa Trieste, Italy):
Prescribing constant curvatures in conformal geometry

 


Thursday, November 8, 2007

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 309

15.15-16.15 Christian Bär (Potsdam):
Conformal structures in non-commutative geometry
16.45-17.45 Burkhard Wilking (Münster):
New Ricci flow invariant curvature conditions

 


Thursday, June 28, 2007

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 05, Room 118

15.15-16.15 Klaus Ecker (FU Berlin):
Mean value formulas for evolving metrics
16.45-17.45 Felix Finster (Regensburg):
Geometry and analysis of asymptotically flat manifolds of small mass

 


Thursday, April 19, 2007

Institut für Differentialgeometrie
Leibniz-Universität Hannover
Welfengarten 1, Main Building, Room F 428

15.15-16.15 Hansjörg Geiges (Köln):
A Bernstein problem for contact spheres
16.45-17.45 Karl Friedrich Siburg (Dortmund):
Symplectic proofs of Borsuk-Ulam type theorems

 


Thursday, January 25, 2007

Institut für Analysis und Numerik
Otto-von-Guericke-Universität Magdeburg
Universitätsplatz 2, Building 02, Room 111

15.15-16.15 Frederic Robert (University of Nice):
Bubbling phenomena for fourth order equations with exponential growth arising from geometry

16.45-17.45 Tobias Lamm (Max Planck Institute for Gravitational Physics, Potsdam-Golm):
Conservation laws for fourth order systems in four dimensions

Thursday, November 2, 2006

Institut für Differentialgeometrie
Leibniz-Universität Hannover Welfengarten 1,
Main Building, Room F 142

15.15-16.15 Steffen Fröhlich (Darmstadt):
Krümmungsabschätzungen und Bernstein-Sätze
für zweidimensionale Immersionen in Euklidischen Räumen
höherer Kodimension
16.45-17.45 Karsten Große-Brauckmann (Darmstadt):
Symmetric constant mean curvature surfaces
Vita
Name: Prof. Dr. Hans-Christoph Grunau

Degrees:

1987 Diploma in Mathematics, University of Göttingen, Germany, Supervisor Prof. Dr. E. Heinz
1990 Dr. rer. nat. (PhD) University of Göttingen, Germany, Supervisor Prof. Dr. E. Heinz
1996 Habilitation, University of Bayreuth

Positions:

1989-1991 Scientific employee, TU Berlin, Germany
1991-2001 Scientific assistant University of Bayreuth, Research Group Prof. Dr. W. von Wahl
2000-2001 Lecturer/Researcher University of Utrecht, Netherlands, on leave from Bayreuth
since 2001 Full Professor for Analysis, University of Magdeburg, Germany
2009-2016 Editor "Jahresbericht der DMV", Member of the Board of the Deutsche Mathematiker-Vereinigung
2016-2020 Dean of the Faculty of Mathematics
Publications

Monograph

Gazzola, F.; Grunau, H.-Ch.; Sweers, G.:
Polyharmonic boundary value problems,
Positivity preserving and nonlinear higher order elliptic equations in bounded domains.
Springer Lecture Notes in Mathematics 1991, Springer-Verlag: Heidelberg etc., 2010.
[Pdf]
[Errata] (as uncovered so far)
Copyright: Springer-Verlag. The original monograph is available on http://link.springer.com/

 


Lecture notes

Grunau, H.-Ch.:
Abbildungsgrad und Fixpunktsätze (Degree of mapping and fixed point theorems),
Vorlesungsausarbeitung, basiert auf Vorlesungen von E. Heinz (Göttingen)
Lecture notes, based upon lectures of E. Heinz (Göttingen)
[Ps] [Pdf]


Textbook

Grauert, H., Grunau, H.-Ch.:
Lineare Algebra und analytische Geometrie,
Copyright: Oldenbourg-Verlag, 1999-2009.
Ab 2009: Alle Rechte bei den Autoren.
[PS-Datei] [DVI-Datei] [PDF-Datei]



 

Habilitationsschrift (1996)
Polyharmonische Dirichletprobleme: Positivität, kritische Exponenten und kritische Dimensionen
[Ps] [Pdf] [Dvi]
English Summary
[Ps] [ Pdf] [Dvi]

 


 

Articles

 

Grunau, H.-Ch.; Romani, G.:
Unexpected differences between fundamental solutions of general higher-order elliptic operators and of products of second-order operators.
[Pdf]

 

Grunau, H.-Ch.:
Boundary Value Problems for the Willmore Functional.
Survey article, submitted to RIMS Kokyuroku series,
Proceedings of the workshop ``Analysis of Shapes of Solutions to Partial Differential Equations'', June 27-29, 2018.
[Pdf]

 

Eichmann, S.; Grunau, H.-Ch.:
Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions.
Adv. Calc. Var., to appear.
[Pdf]
Copyright: de Gruyter. The original article is available on https://www.degruyter.com/view/j/acv

 

Dipierro, S.; Grunau, H.-Ch.:
Boggio's formula for fractional polyharmonic Dirichlet problems.
Ann. Mat. Pura Appl. (1923-) 196, 1327-1344 (2017).
[Pdf]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

 

Deckelnick, K.; Grunau, H.-Ch.; Röger, M:
Minimising a relaxed Willmore functional for graphs subject to boundary conditions.
Interfaces Free Bound. 19, 109-140 (2017).
[Pdf]
Copyright: EMS - European Mathematical Society Publishing House.
The original article is available on https://www.ems-ph.org/journals/journal.php?jrn=ifb

Grunau, H.-Ch.; Lenor, St.:
Uniform estimates and convexity in capillary surfaces.
Nonlinear Analysis A: T.M.A. 97, 83-93 (2014).
[Pdf]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

Grunau, H.-Ch.; Sweers, G.:
In any dimension a "clamped plate" with a uniform weight may change sign.
Nonlinear Analysis A: T.M.A. 97, 119-124 (2014).
[Pdf]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

 

Grunau, H.-Ch.; Sweers, G.:
A clamped plate with a uniform weight may change sign.
Discrete Cont. Dynam. Systems - S (Proceedings etc.) 7, 761 - 766 (2014)
[Pdf]
Copyright: American Institute of Mathematical Sciences, first published with AIMS Press.

 

Grunau, H.-Ch.; Robert, F.:
Uniform estimates for polyharmonic Green functions in domains with small holes.
In: J. Serrin, E. Mitidieri, V. Radulescu (eds.), Recent Trends in Nonlinear Partial Differential Equations II: Stationary Problems.
Contemporary Mathematics 595, 263-272 (2013).
[Ps] [Pdf] [Dvi]
Copyright: American Mathematical Society. The original article is available on http://www.ams.org/books/conm/595/

 

Grunau, H.-Ch.:
The asymptotic shape of a boundary layer of symmetric Willmore surfaces of revolution.
In: C. Bandle et al. (eds.), Inequalities and Applications 2010.
International Series of Numerical Mathematics 161, 19-29 (2012).
[Ps] [Pdf]
Copyright: Springer Basel. The original article is available on http://link.springer.com/

 

Grunau, H.-Ch.; Robert, F.; Sweers, G.:
Optimal estimates from below for biharmonic Green functions.
Proc. Amer. Math. Society 139, 2151-2161 (2011).
[Pdf]
Copyright: American Mathematical Society AMS. The original article is available on http://www.ams.org/journals/proc/

 

Gazzola, F.; Grunau, H.-Ch.; Sweers, G.:
Optimal Sobolev and Hardy-Rellich constants under Navier boundary conditions.
Ann. Mat. Pura Appl. 189, 475-486 (2010).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

 

Dall'Acqua, A., Fröhlich, St., Grunau, H.-Ch., Schieweck, F.:
Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data.
Adv. Calc. Var. 4, 1-81 (2011).
[Ps] [Pdf]
Copyright: de Gruyter. The original article is available on https://www.degruyter.com/view/j/acv

 

Grunau, H.-Ch.:
Nonlinear questions in clamped plate models (Survey article).
Milan J. Math. 77, 171-204 (2009).
[Ps.gz] [Pdf]
Copyright: Birkhäuser-Verlag. The original article is available on http://link.springer.com/

 

Deckelnick, K. , Grunau, H.-Ch.:
A Navier boundary value problem for Willmore surfaces of revolution.
Analysis 29, 229-258 (2009).
[Ps] [Pdf]
Copyright: de Gruyter. The original article is available on http://www.degruyter.com/

 

Gazzola, F., Grunau, H.-Ch.:
Some new properties of biharmonic heat kernels.
Nonlinear Analysis T.M.A. 70, 2965 - 2973 (2009).
[Ps] [Pdf] [Dvi]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

 

Dall'Acqua, A., Deckelnick, K., Grunau, H.-Ch.:
Classical solutions to the Dirichlet problem for Willmore surfaces of revolution.
Adv. Calc. Var. 1, 379 - 397 (2008).
[Ps] [Pdf] [Dvi]
Copyright: de Gruyter. The original article is available on https://www.degruyter.com/view/j/acv

 

Ferrero, A., Grunau, H.-Ch., Karageorgis, P.:
Supercritical biharmonic equations with power-type nonlinearity.
Ann. Mat. Pura Appl. 188, 171 - 185 (2009).
[Ps] [Pdf] [Dvi], http://arxiv.org/abs/0711.2202
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

 

Ferrero, A., Gazzola, F., Grunau, H.-Ch.:
Decay and eventual local positivity for biharmonic parabolic equations.
Discrete Cont. Dynam. Systems 21, 1129 - 1157 (2008).
[Ps] [Pdf] [Dvi]
Copyright: American Institute of Mathematical Sciences, first published with AIMS Press.

 

Deckelnick, K., Grunau, H.-Ch.:
Stability and symmetry in the Navier problem for the one-dimensional Willmore equation.
SIAM J. Math. Anal. 40, 2055 - 2076 (2009).
[Ps] [Pdf]
Copyright: SIAM. The original article is available on http://epubs.siam.org/SIMA/sima_toc.html

 

Grunau, H.-Ch., Robert, F.:
Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions.
Arch. Rational Mech. Anal., 195, 865-898 (2010).
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

 

Preprint versions:
Stability of the positivity of biharmonic Green's functions under perturbations of the domain.
[Ps] [Pdf] [Dvi],
Positivity issues of biharmonic Green's functions under Dirichlet boundary conditions.
[Ps] [Pdf] [Dvi], http://arxiv.org/abs/0705.3301Research announcement:
Boundedness of the negative part of biharmonic Green's functions under Dirichlet boundary conditions in general domains.
C. R. Math. Acad. Sci. Paris , Ser. I 347, 163 - 166 (2009).
Copyright: Academie des Sciences / Elsevier Masson SAS.
The article is available on http://www.sciencedirect.com/science/journal/1631073X.

 

Gazzola, F., Grunau, H.-Ch.:
Local eventual positivity for a biharmonic heat equation in R^n.
Discrete Cont. Dynam. Systems - S (Proceedings etc.) 1, 83 - 87 (2008).
[Ps] [Pdf] [Dvi]
Copyright: American Institute of Mathematical Sciences, first published with AIMS Press.

 

Grunau, H.-Ch., Ould Ahmedou, M., Reichel, W.:
The Paneitz equation in hyperbolic space.
Annales Inst. H. Poincare (C) Nonlinear Analysis 25, 847 - 864 (2008).
[Ps] [Pdf] [Dvi]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

 

Ferrero, A., Grunau, H.-Ch.:
The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity.
J. Differ. Equations 234, 582 - 606 (2007).
[Ps] [Pdf] [Dvi]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

 

Arioli, G., Gazzola, F., Grunau, H.-Ch., Sassone, E.:
The second bifurcation branch for radial solutions of the Brezis-Nirenberg problem in dimension four.
Nonl. Differ. Equ. Appl. NoDEA 15, 69-90 (2008).
[Ps] [Pdf] [Files for computer assisted proof]
Copyright: Birkhäuser-Verlag. The original article is available on http://link.springer.com/

 

Grunau, H.-Ch., Sweers, G.:
Regions of positivity for polyharmonic Green functions in arbitrary domains.
Proc. Amer. Math. Society 135, 3537-3546 (2007).
[Ps] [Pdf] [Dvi]
Copyright: AMS. The original article is available on http://www.ams.org/journals/proc/

 

Berchio, E., Grunau, H.-Ch.:
Local regularity of weak solutions of semilinear parabolic systems with critical growth.
J. Evolution equations 7, 177-196 (2007).
[Ps] [Pdf] [Dvi]
Copyright: Birkhäuser-Verlag. The original article is available on http://link.springer.com/

 

Gazzola, F., Grunau, H.-Ch.:
Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay.
Calc. Var. 30, 389-415 (2007).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

 

Arioli, G., Gazzola, F., Grunau, H.-Ch.:
Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity.
J. Differ. Equations 230, 743 - 770 (2006).
[Ps] [Pdf] [Files for computer assisted proof]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

 

Deckelnick, K., Grunau, H.-Ch.:
Boundary value problems for the one-dimensional Willmore equation,
Calc. Var. 30, 293-314 (2007).
[Ps] [Pdf]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/
Preliminary and more special version: Technical Report 05-02, University of Magdeburg.
[Ps] [Pdf]

 

Gazzola, F., Grunau, H.-Ch.:
Radial entire solutions for supercritical biharmonic equations.
Math. Annal. 334, 905 - 936 (2006).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

 

Grunau, H.-Ch., Kühnel, M.:
On the existence of Hermitian-harmonic maps from complete Hermitian to complete Riemannian manifolds,
Math. Z. 249, 297-327 (2005).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

 

Arioli, G., Gazzola, F., Grunau, H.-Ch., Mitidieri, E.:
A semilinear fourth order elliptic problem with exponential nonlinearity,
SIAM J. Math. Anal. 36, 1226-1258 (2005).
[Ps] [Pdf] [Files for computer assisted proof]
Copyright: SIAM. The original article is available on http://www.siam.org/journals/sima/sima.htm

 

Dall'Acqua, A., Grunau, H.-Ch., Sweers, G.:
On a conditioned Brownian motion and a maximum principle on the disk,
J. Anal. 93, 309-329 (2004).
[Ps] [Pdf] [Dvi]

 

Gazzola, F., Grunau, H.-Ch., Squassina, M.:
Existence and nonexistence results for critical growth biharmonic elliptic equations,
Calc. Var. PDE 18, 117-143 (2003).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/       

 

Gazzola, F., Grunau, H.-Ch., Mitidieri, E.:
Hardy inequalities with optimal constants and remainder terms,
Transactions Amer. Math. Soc. 356, 2149-2168 (2004).
[Ps] [Pdf] [Dvi]
Copyright: AMS. The original article is available on http://www.ams.org/tran/

 

Grunau, H.-Ch., Sweers, G.:
Optimal conditions for anti-maximum principles,
Ann. Sc. Norm. Sup. Pisa. Cl. Sci. (4) 30, 499-513 (2001)

 

Grunau, H.-Ch.:
Positivity, change of sign and buckling eigenvalues in a one-dimensional fourth order model problem,
Adv. Differ. Equations. 7, 177-196 (2002).
[Ps] [Pdf]
Copyright: Khayyam-Publishing http://projecteuclid.org/euclid.ade/

 

Grunau, H.-Ch., Sweers, G.:
Sharp estimates for iterated Green functions,
Proc. Royal Soc. Edinburgh. 132A, 91-120 (2002).
[Ps] [Pdf] [Dvi]
This article is reproduced by permission of the Royal Society of Edinburgh.
The original article is available on http://ninetta.ingentaselect.com/

 

Grunau, H.-Ch., Sweers, G.:
Nonexistence of local minima of supersolutions for the circular clamped plate,
Pacific J. Math 198, 437-442 (2001).
[Ps] [Pdf] [Dvi]
The original article is available on http://msp.org/pjm/

 

Gazzola, F., Grunau, H.-Ch.:
Critical dimensions and higher order Sobolev inequalities with remainder terms,
Nonl. Differ. Equ. Appl. NoDEA 8, 35-44 (2001).
[Ps] [Pdf] [Dvi]
Copyright: Birkhäuser-Verlag. The original article is available on http://link.springer.com/

 

Gazzola, F., Grunau, H.-Ch.:
On the role of space dimension $n=2+2sqrt{2}$ in the semilinear Brezis-Nirenberg eigenvalue problem,
Analysis 20, 395-399 (2000).
[Ps] [Pdf] [Dvi]
Copyright: de Gruyter http://www.degruyter.com

 

Grunau, H.-Ch., Sweers, G.:
Sign change for the Green function and for the first eigenfunction of equations of clamped plate type,
Archive Rational Mech. Anal. 150, 179-190 (1999).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

 

Grunau, H.-Ch.:
L^p-decay rates for strong solutions of a perturbed Navier-Stokes system in R^3, in: J. G. Heywood, K. Masuda, R. Rautmann, V. A. Solonnikov (eds.),
Theory of the Navier-Stokes Equations, Series Adv. Math. Appl. Sciences 47, 64-71 (1998).

 

Grunau, H.-Ch., Sweers, G.:
The role of positive boundary data in generalized clamped plate equations,
Z. angew. Math. Phys., 49, 420-435 (1998).
[Ps] [Pdf] [Dvi]
Copyright: Birkhäuser-Verlag. The original article is available on http://link.springer.com/

 

Grunau, H.-Ch., Sweers, G.:
Maximum principles and positive principal eigenfunctions for polyharmonic equations, in: G. Caristi, E. Mitidieri (eds.),
Reaction Diffusion Systems, Lecture Notes in Pure and Applied Mathematics 194, 163-182 (1998).

 

Grunau, H.-Ch.:
Uniqueness of small solutions to the Dirichlet problem for the higher dimensional H-system,
Rocky Mountain J. Math. 27, 801-815 (1997).

 

Grunau, H.-Ch., Sweers, G.:
Positivity properties of elliptic boundary value problems of higher order,
Proc. 2nd World Congress of Nonlinear Analysis, Nonlinear Anal., T. M. A. 30, 5251-5258 (1997).

 

Grunau, H.-Ch., Wahl, W. von:
Regularity considerations for semilinear parabolic systems,
Rend. Istit. Mat. Univ. Trieste 28 (Suppl.), 221-233 (1997).

 

Grunau, H.-Ch., Sweers, G.:
Classical solutions for some higher order semilinear elliptic equations under weak growth conditions,
Nonlinear Anal., T.M.A. 28, 799-807 (1997).

 

Grunau, H.-Ch., Sweers, G.:
Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions,
Math. Ann. 307, 589-626 (1997).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

 

Grunau, H.-Ch.:
On a conjecture of P. Pucci and J. Serrin,
Analysis 16, 399-403 (1996).
[Ps] [Pdf] [Dvi]
Copyright: de Gruyter http://www.degruyter.com

 

Grunau, H.-Ch., Sweers, G.:
Positivity for perturbations of polyharmonic operators with Dirichlet boundary conditions in two dimensions,
Math. Nachr. 179, 89-102 (1996).
[Ps] [Pdf] [Dvi]
Copyright: Mathematische Nachrichten, Wiley Verlag http://www.wiley-vch.de/

 

Grunau, H.-Ch.:
Critical exponents and multiple critical dimensions for polyharmonic operators. II,
Boll. Unione Mat. Ital.(7) 9-B, 815-847 (1995).

 

Grunau, H.-Ch.:
Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents,
Calculus of Variations and PDE3, 243-252 (1995).

 

Bernis, F., Grunau, H.-Ch.:
Critical exponents and multiple critical dimensions for polyharmonic operators,
J. Differ. Equations117, 469-486 (1995).

 

Grunau, H.-Ch., Wahl, W. von:
Regularity of weak solutions of semilinear parabolic systems of arbitrary order,
Journal d'Analyse 62, 307-322 (1994).
[Ps] [Pdf] [Dvi]

 

Grunau, H.-Ch.:
L^2-decay rates for weak solutions of a perturbed Navier-Stokes system in R^3,
J. Math. Anal. Appl. 185, 340-349 (1994).

 

Grunau, H.-Ch.:
The Reynolds number and large time behaviour for weak solutions of the Navier-Stokes equations,
Z. angew. Math. Phys. 44, 587-593 (1993).

 

Grunau, H.-Ch.:
Boundedness for large |x| of suitable weak solutions of the Navier-Stokes equations with prescribed velocity at infinity,
Commun. Math. Phys. 151, 577-587 (1993).
[Pdf]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

 

Grunau, H.-Ch.:
The Dirichlet problem for some semilinear elliptic differential equations of arbitrary order,
Analysis 11, 83-90 (1991).

 

 

 

 

 

 

 

 

 
Lectures
Team
Research Interests


These lectures gives an impression of my present research interests: Marburg, Perugia, Nizza .

Boundary value problems for Willmore surfaces

The Willmore equation, i.e. the Euler-Lagrange equation of the Willmore functional, is a particularly challenging and important problem in nonlinear analysis. It is quasilinear and of fourth order. Many methods which are well established in second order problems do not apply any longer. Nevertheless, significant progress could be achieved in the past years e.g. by L. Simon, E. Kuwert, R. Schätzle, T. Riviere and many others. Most of these results, however, concern closed surfaces. As for boundary value problems only little is known so far since very hard compactness difficulties have to be overcome. By means of numerical studies and analytical investigations we want to study first quite symmetric prototype situations in order to outline in which direction one may expect to obtain a-priorily bounded minimising sequences and classical solutions. Our student Stephan Lenor has produced a number of pictures. This is a joint project with my colleagues Klaus Deckelnick und Friedhelm Schieweck who intend to develop numerical algorithms and convergence results also in more general situations, e.g. for graphs over two dimensional domains. Analysis, numerical analysis and numerics will intensively interact.
Supported by Deutsche Forschungsgemeinschaft, 1.10.2008-30.09.2010. Anna Dall'Acqua was working on this project.

Qualitative properties of solutions of elliptic boundary value problems of higher order

Here one may think of the clamped plate equation (biharmonic operator under Dirichlet boundary
conditions) as the most simple prototype for higher order elliptic boundary value problems. Of particular interest are positivity preserving properties of the corresponding solution operators:
Is it possible to find conditions on the domain and the differential operator such that positive data always yield positive solutions? Even for the "simple" example of the clamped plate equation it is up to now not possible to answer this question completely. There are as well examples of domains with positivity preserving as of domains, where change of sign occurs. I am mainly interested in the first class of domains: In two dimensions, e.g., in domains close to the disk, positive right hand sides always give rise to positive solutions. "Upwards pushing yields upwards bending."

Positivity properties of linear boundary value problems are not only of interest on their own, but one may also try to apply them to nonlinear problems. Although first results could be achieved it is still by far not obvious to what extent the (relatively restricted) positivity results will be of use for general nonlinear elliptic boundary value problems of higher order. I hope for some progress in problems from physics (mechanics, hydrodynamics) and differential geometry.

In this field I collaborate with Guido Sweers (Cologne, TU Delft) and Frederic Robert.

 

Semilinear eigenvalue problems involving critical Sobolev exponents

These equations are closely related to problems in conformal geometry. Here we are basing upon two widely known papers of Brezis-Nirenberg and Pucci-Serrin and try to find out in how far the results kown for second order problems extend to boundary value problems of higher order. Emphasis is laid on the interplay with qualitative properties of solutions. In this connection a modified version of a conjecture of Pucci and Serrin concerning the "critical dimension phenomenon" for semilinear polyharmonic problems could be proved.  A full proof of the original conjecture, however, seems up to now out of reach.
Recently, the connections with the above mentioned positivity properties could be more intensively exploited. Here a decomposition method with respect to pairs of dual cones in higher order Sobolev spaces has proved to be particularly useful. This method replaces the decomposition in positive and negative part, which is no longer admissible in these spaces. In this way, compactness properties of the corresponding variational functionals could be described efficiently.
In this field I am particularly working with Filippo Gazzola.

 

Biharmonic equations with supercritical growth

Variational techniques are no longer available. Instead, comparison principles, the sub-/supersolution method or in the case of radially symmetric solutions methods from dynamical systems have to be applied. Combining supercritical growth with differential operators of higher order gives rise to subtle technical problems. Also here, I collaborate with Filippo Gazzola, which was 2005 and 2006 supported by the Vigoni-programme of DAAD (Bonn) and CRUI (ROM).

 

Parabolic systems with critical growth

Under consideration are semilinear systems, whose nonlinear terms grow critically with respect to the canonical energy norm of weak solutions, i.e. we are dealing with controllable growth conditions.
Without further assumptions (like e.g. sign conditions on the nonlinear term) it was shown in a joint paper with Wolf von Wahl that every weak solution is regular. For this result we crucially employ a continuity method with the time as parameter of continuity.
Further, we consider geometric evolution equations in order to construct Hermitian harmonic mappings between noncompact complete manifolds. This semilinear system has quadratic growth with respect to the gradient and is not in divergence form.

 

Navier-Stokes equations

Here I am interested in instationary problems in exterior domains with nonzero prescribed velocity at infinity. I have been investigating regularity of suitable weak solutions and the asymptotic behaviour, as the time tends to infinity, of perturbations of physically reasonable stationary solutions with small energetic Reynolds number.
 

 

Selected Theses of Students
Meister, Ch.:
L^p - L^q - Theorie und asymptotisches Verhalten der Störungsenergie bei einem Navier-Stokes-System im Außenraum mit Anströmgeschwindigkeit für kleine Reynoldszahlen
Dissertation, Universität Bayreuth, 2001.
[Pdf]
Bräu, T.:
Eine Zerlegungsmethode bzgl. Paaren zueinander dualer Kegel und Anwendung in Sobolevräumen höherer Ordnung
Studienarbeit, Universität Magdeburg, 2005.
[Pdf]
English translation: A decomposition method with respect to dual cones and its application to higher order Sobolev spaces
Seminar paper, University of Magdeburg, 2005.
[Pdf]
Köckritz, Ch.:
Lokale Positivität der polyharmonischen Greenschen Funktion
Studienarbeit, Universität Magdeburg, 2007.
[Pdf]
Jachalski, S.:
Asymptotic behaviour for Willmore surfaces of revolution under natural boundary conditions
Englisches Preprint, Teil der Diplomarbeit, Universität Magdeburg, 2010.
[Pdf]
Pulst, L.:
Ein Analogon eines Satzes von Moser auf der S^4
Diplomarbeit, Universität Magdeburg, 2010.
[Pdf]
Lenor, S.:
Konvexität und gleichmäßige Abschätzungen bei der Kapillaritätsgleichung
Diplomarbeit, Universität Magdeburg, 2012.
[Pdf]
Eichmann, S.:
Nichtperiodische Fortsetzbarkeit von Willmore-Flächen unter Axialsymmetrie
Diplomarbeit, Universität Magdeburg, 2014.
[Pdf]
Gulyak, B.:
Erste a-priori-Abschätzungen für Willmore-Graphen über allgemeinen Gebieten
Projektarbeit, Universität Magdeburg, 2014.
[Pdf]
Doemeland, M.
Verallgemeinerung eines Existenzsatzes für axialsymmetrische Minimierer des Willmore-Funktionals auf das Helfrich-Funktional
Projektarbeit, Universität Magdeburg, 2015.
[Pdf]
Pulst, L.:
Dominance of positivity of the Green's function associated to a perturbed polyharmonic Dirichlet boundary value problem by pointwise estimates
PhD Dissertation, Universität Magdeburg, 2015.
[Pdf]
Barlage, E.:
Positive Lösungen elliptischer Gleichungen zweiter Ordnung mit kritischem Wachstum in kontrahierbaren Gebieten
Masterarbeit, Universität Magdeburg, 2017.
[Pdf]
Eichmann, S.:
Willmore Surfaces of Revolution Satisfying Dirichlet Data
Dissertation, Universität Magdeburg, 2017.
[Pdf]
Himmel, B.:
Die Boggio-Formel für polyharmonische Dirichletprobleme
Bachelorarbeit, Universität Magdeburg, 2019.
[PDF]

 

I disclaim responsibility for the contents of web sites of third parties, which are linked to my websites.
No liability for the information provided on my websites.

 

 

 

Course Material

Buch mit Hans Grauert "Lineare Algebra und Analytische Geometrie"

Copyright: Oldenbourg-Verlag, München, 1999-2009.
Ab 2009: Alle Rechte bei den Autoren.


Kompletter Download: [ PS-Datei] [ DVI-Datei] [ PDF-Datei]


 

Vorlesungsmanuskript "Abbildungsgrad und Fixpunktsätze"

[ PS-Datei] [ DVI-Datei] [ PDF-Datei]


 

Algorithmische Mathematik: Beispielprogramme


Paragraph 1
[ Additionsmaschine1.c] [ Additionsmaschine2.c] [ Additionsmaschine2a.c] [ Additionsmaschine2b.c]
[ Additionsmaschine2c.c] [ Fakultaet.c] [ Taschenrechner.c]
Paragraph 2
[ ggT.c] [ Primfaktorzerlegung.c]
Paragraph 3
[ Einheiten_in_Z_mod_mZ.c] [ Chin_Restsatz.c]
Paragraph 4
[ Einlesen_strings.c] [ Einlesen_lange_strings.c] [ Liste_einfach.c] [ Liste_doppelt_verkettet.c] [ Addition_lang.c]
Paragraph 5
[ Breitensuche.c] [ Abstandsbestimmung.c]
Paragraph 6
[ Bellman_Ford.c] [ Dijkstra.c]
Paragraph 7
[ Exponentialfunktion1.c] [ Exponentialfunktion2.c] [ Exponentialfunktion3.c] [ Exponentialfunktion4.c]
[ Logarithmus1.c] [ Logarithmus2.c] [ Cordic_Division.c]
Gnuplot-Interface von N. Devillard: [ gnuplot_i.c] [ gnuplot_i.h] [ gnuplot_i.o]
[ Kompilierungskommandos.txt]
Paragraph 8
[ Logarithmus_bisek.c] [ Min_Max_a.c] [ Min_Max_b.c] [ Wurzel1.c] [ Wurzel2.c] [ Kompilierungskommandos.txt]
Paragraph 9
[ Differentiation1.c] [ Differentiation2.c] [ Integration1.c] [ Integration2.c] [ Kompilierungskommandos.txt]


Übungen:
Web-Seite von Herrn Ludwig Pulst


 

Maple-Worksheets zu Lineare Algebra I


Grundlagen: Matrizenkalkül, Gaußscher Algorithmus
[ Grundlagen.mws]
Trigonalisierung beliebiger komplexer qudratischer Matrizen mittels unitärer Koordinatenwechsel
[ Trigonalisierung.mws]
Vertiefung: Determinanten, Eigenwerte, Eigenvektoren, Diagonalisierung
[ Vertiefung.mws]


 

Maple-Worksheets zu Analysis I

(erstellt von Frau Stephanie Lehmann und Frau Elke Eisenschmidt)

Zur Konvergenz von Folgen
[ Folgen.mws]
Polarkoordinaten
[ Komplex.mws]
Stetigkeit
[ Stetig.mws]
Kurvendiskussion und Differentialrechnung
[ Differentialrechnung.mws]


 

Maple-Worksheets zu Analysis II


Unstetigkeitsverhalten von Funktionen zweier Veränderlicher
[ Unstetig.mws]
Zur Integration
[ Integration.mws]
Kurven und Ableitungen von Funktionen mehrerer Veränderlicher
[ PartielleAbleitung.mws]
Implizite Funktionen
[ ImpliziteFunktion.mws]


 

Maple-Worksheets zu Mathematik für Physiker III/IV


Fourierreihen
[ fourierseries2.mws]


 

Maple-Worksheets zu Funktionentheorie


Hier gibt es ein aktuelles Lehrbuch, welches die theoretische Entwicklung des Stoffs mit zahlreichen Maple-Worksheets auf sehr gelungene Weise unterstützt und illustriert:
W. Forst, D. Hoffmann,
Funktionentheorie erkunden mit Maple, Springer-Verlag: Berlin etc. 2002.
Die zugehörigen Worksheets können auf der Homepage von Herrn Kollegen W. Forst (Ulm) heruntergeladen werden.


 

Maple-Worksheets zu Partielle Differentialgleichungen

(Animationen für Laplace-, Wellen- und Wärmeleitungsgleichung mittels Fourierreihenentwicklung)

Laplacegleichung
[ poissonkernel.mws]
Wärmeleitungsgleichung räumlich eindimensional
[ heatfourier.mws]
Wärmeleitungsgleichung räumlich zweidimensional, Quadrat
[ heatfourier2D_1.mws]
Wellengleichung räumlich eindimensional
[ wavefourier.mws]
Wellengleichung räumlich zweidimensional, Quadrat
[ wavefourier2D_1.mws]
Wellengleichung räumlich zweidimensional, Kreis
[ wavefourier2D_2.mws]
Wellengleichung räumlich zweidimensional, Kreis, radialsymmetrisch
[ wavefourier2D_2radial.mws]


 

Aufgaben Algorithmische Mathematik I (Wintersemester 2012/13)


[ PDF-Datei]

Aufgaben Algorithmische Mathematik II (Sommersemester 2012/13)


[ PDF-Datei]


 

Aufgaben Analysis I (Wintersemester 2010/11)


[ PDF-Datei]

Aufgaben Analysis II (Sommersemester 2011)


[ PDF-Datei]

Aufgaben Analysis III (Wintersemester 2011/12)


[ PDF-Datei]


 

Aufgaben zu Funktionentheorie (Sommersemester 2012)


[ PDF-Datei]


 

Aufgaben Partielle Differentialgleichungen I


[ PDF-Datei]

Aufgaben Partielle Differentialgleichungen II


[ PDF-Datei]


 

Aufgaben Differentialgeometrie I (Wintersemester 2012/13)


[ PDF-Datei]

Aufgaben Differentialgeometrie II (Sommersemester 2012/13)


[ PDF-Datei]


 

Aufgaben Dynamische Systeme


[ PS-Datei] [ DVI-Datei] [ PDF-Datei]


 

Aufgaben zu "Analysis der Navier-Stokes-Gleichungen"


[ PS-Datei] [ DVI-Datei] [ PDF-Datei]


 

Aufgaben zu Abbildungsgrad und Fixpunktsätze


[ PS-Datei] [ DVI-Datei] [ PDF-Datei]

Lösungen dazu


[ PS-Datei] [ DVI-Datei] [ PDF-Datei]


 

Aufgaben zu Lineare Algebra I für Physiker


[ PS-Datei] [ DVI-Datei] [ PDF-Datei]

Aufgaben zu Mathematik III für Physiker


[ PS-Datei] [ DVI-Datei] [ PDF-Datei]

Aufgaben zu Mathematik IV für Physiker


[ PS-Datei] [ DVI-Datei] [ PDF-Datei]
 
 



Keine Haftung für die Inhalte von Internetseiten Dritter, die mit meinen Internetseiten verlinkt sind.
Alle Angaben auf meinen Internetseiten ohne Gewähr.

Last Modification: 24.04.2019 - Contact Person: Hans-Christoph Grunau