Talk by Robert Denk

Motivated by model uncertainty and stochastic optimal control problems, we develop a general theory of nonlinear semigroups in spaces of continuous functions. In contrast to the linear theory, the domain of the generator is in general not invariant under the semigroup. Therefore, we replace the domain by a larger Lipschitz set and the norm convergence by $\Gamma$-convergence. We obtain invariance of the Lipschitz set, a comparison principle for nonlinear semigroups, and results on approximation by smooth functions. The applications include fully nonlinear partial differential equations arising from parameter uncertainty and Wasserstein perturbations of transition and heat semigroups.

This talk is based on joint work with Jonas Blessing, Michael Kupper (both Konstanz), and Max Nendel (Bielefeld).