Research Group Non-linear Partial Differential Equations and Geometric Analysis

 

Professors and Lecturers

 

Prof. Dr. K. Deckelnick

Prof. Dr. H.-Ch. Grunau

Priv.-Doz. Dr. B. Rummler

Prof. Dr. M. Simon

 

 

Research Assistants

 

M.Sc. Boris Gulyak  

Dr. Jiawei Liu

M.Sc. Wolfgang Meiser

M.Sc. Alina Mierswa

 

 

Research Interests

 

Boundary value problems for Willmore surfaces
  • Estimates, qualitative properties & existence (Deckelnick, Grunau)
  • Development and analysis of numerical approximation methods (Deckelnick)

 

Ricci-flow (Simon)
  • Behaviour of singularities
  • Existence and regularity in case of non-smooth initial data

 

Elliptic boundary value problems of higher order (Grunau)
  • Almost positivity and estimates of Green's functions
  • Semilinear equations with (super) critical growth, related to differential geometry

 

Optimal control problems with partial differential equations (Deckelnick)
  • Development & analysis of numerical approximation methods
  • Applications to parameter identification problems

 

Nonlinear evolution equations
  • Existence, Qualitative Properties & Numerical Approximation for Geometric Evolution Equations (Deckelnick)
  • Stability and estimates, almost positivity (Grunau / Simon)
  • Existence & regularity on non-smooth starting dates (Simon)

 

Hydrodynamics (Rummler)
  • Eigenfunctions of the Stokes operator
  • Laminar-turbulent transition behaviour, bifurcations
  • Regularity of decomposition fields

 

 

Research Seminar

Monday, 15:00-17:00, G03-214

Seminar on Differential Geometry and Anaylsis

 

current lectures / archive