Our research concerns mainly nonlinear Partial Differential Equations (PDE) including e.g. the p-Laplace and the Monge-Ampère equations, as well as integro-differential equations (non-local PDEs). Such PDEs have connections to minimization problems, nonlinear elasticity theory, fluid dynamics, stochastic games, image processing, differential geometry, meteorology, optics, interface evolution and kinetic theory. Monge-Ampère equations are linked to optimal transport which has applications in machine learning, signal processing, probability theory and statistics. Some typical problems we study are the existence and uniqueness of viscosity solutions, variational principles, boundary behaviour, asymptotic behaviour for large times, strong maximum and minimum principles, Phragmen-Lindelöf theorems, construction of explicit solutions, well posedness for system of PDEs with obstacles having applications to optimization problems such as e.g. managing a chain of hydropower plants and pattern formation.
