Research

Our research focuses on the field of applied analysis, more precisely the variational calculus and the theory of non-linear partial differential equations. The problems are mostly motivated by questions from applications, for example in materials sience, geosciences, image processing, and more recently also the theory of machine learning.

We  development new methods for the treatment of variational multi-scale problems,  and address in particular,

•  Non-convex variational problems,  notions of convexity, relaxation
•  Asymptotic analysis, Gamma-convergence, dimension reduction, homogenization
•  PDE constraints, differential inclusions
•  Rigidity, nonlocality
•  Mathematical models in the theory of elasticity and plasticity

We acknowledge the support by the Bavarian Research Alliance through the  BayIntAn project "Varying horizons: Mathematical foundation of new material models with non-local energies". From 2019-2022, part of our research activities were funded by the Dutch Organization for Scientific Research (NWO) through the TOP2 project "Variational methods for multiscale problems: The interplay of rigidity and anisotropic geometries".