Research

The field of research in my group is nonlinear analysis and related applications, in particular:

•   calculus of variations
•   partial differential equations
•   theory of critical points
•   nonlinear elasticity and critical points
•   mathematical foundations of continuum mechanics
•   numerics of nonsmooth problems

More precisely, highly degenerate partial differential equations related to nonsmooth variational problems are treated. Here we consider elliptic problems as, e.g., the eigenvalue problem for the 1-Laplacian but also free boundary value problems related to contact problems in nonlinear elasticity. In addition to analytical investigations, numerical schemes for such problems are developed and implemented. Moreover, for a better description of concentration phenomena, a new mathematical approach to the foundations of continuum mechanics has been developed.