Research

Research Interests

The main focus of our research is on elliptic and parabolic partial differential equations of p-Laplacian and porous medium type, including the case p equals one (total variation flow). These equations are connected to many different applications, such as diffusion in nonhomogeneous media, gas or fluids in porous media, turbulent filtration through porous media, non-Newtonian fluids and imaging.

  • Elliptic and parabolic equations and systems
  • Evolutionary equations/systems with degenerate or singular diffusion
  • Total variation flow
  • Existence of weak solutions by variational methods
  • Global and local properties (regularity, higher integrability, etc.)
  • Analysis in metric measure spaces
  • Nonlinear Potential Theory
  • Calculus of Variations
  • Geometric Measure Theory

Thesis

We are pleased to discuss possible topics for your bachelor, master, and doctor thesis.

Possible Supervisors

Prof. Dr. Frank Duzaar (master and doctor thesis)

PD Dr. Jens Habermann (bachelor, master, and doctor thesis)