Publikationen

 

Monograph

neues buch

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] [Dvi] Lehrbuch

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.: The Dirichlet problem for some semilinear elliptic differential equations of arbitrary order,
Analysis 11, 83-90 (1991).
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 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.: 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., Wahl, W. von: Regularity of weak solutions of semilinear parabolic systems of arbitrary order,
Journal d'Analyse 62, 307-322 (1994).
[Ps] [Pdf] [Dvi]
Bernis, F., Grunau, H.-Ch.: Critical exponents and multiple critical dimensions for polyharmonic operators,
J. Differ. Equations 117, 469-486 (1995).
Grunau, H.-Ch.: Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents,
Calculus of Variations and PDE 3, 243-252 (1995).
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., 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.: 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 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., 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., Wahl, W. von: Regularity considerations for semilinear parabolic systems,
Rend. Istit. Mat. Univ. Trieste 28 (Suppl.), 221-233 (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.: 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.: 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., 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.: 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.: 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/
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.: 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/
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.: 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.: Optimal conditions for anti-maximum principles,
Ann. Sc. Norm. Sup. Pisa. Cl. Sci. (4) 30, 499-513 (2001).
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/
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/
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]
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
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/
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/
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]
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/
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/
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/
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/
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/
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/
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/
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.
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/0705.3301
Research 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.
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/
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
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., 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
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/
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/
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/
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/
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.: 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.; 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.; 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.; 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/
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

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/

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
 
  Die herunterladbaren Dateien sind Preprintversionen der entsprechenden Arbeiten und können sich im Detail von diesen unterscheiden.
The downloadable files are preprint versions of the corresponding articles and may differ from these in some details.
Keine Haftung für die Inhalte von Internetseiten Dritter, die mit meinen Internetseiten verlinkt sind.
Alle Angaben auf meinen Internetseiten ohne Gewähr.
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.

Letzte Änderung: 01.03.2018 - Ansprechpartner:

Sie können eine Nachricht versenden an: Webmaster
Sicherheitsabfrage:
Captcha
 
Lösung: