Geometric Partial Differential Equations
The research group „Geometric Partial Differential Equations“ employs analysis methods and works in the calculus of variations, on non-linear partial differential equations, in geometric measure theory, and in regularity theory. The focus is on:
- boundary value problems and obstacle problems for BV functions, sets of finite perimeter, and currents around the Plateau problem, the least gradient problem, and the Mumford-Shah functional,
- (quasi)convex variational integrals, quasi-linear elliptic PDE systems and PDEs with degenerate or non-uniform ellipticity of minimal surface, p-Laplace or Monge-Ampère type
Typical questions deal with existence, uniqueness, and characterizations of (generalized) solutions, with Lp estimates and partial regularity, and with convex duality.