Ulisse Stefanelli: Existence for doubly nonlinear SPDEs

Speaker
Unlisse Stefanelli, University of Vienna

Abstract
I intend to present some recent results on the existence of probabilistic weak solutions to doubly nonlinear parabolic stochastic PDEs. Both classes of doubly nonlinear equations can be considered, even including the degenerate rate-independent case. A classical viscous regularization approach, combined with smoothing and, possibly, with a time-rescaling argument, provides approximate solutions. By passing to the limit in the approximation, one obtains martingale solutions. In case of uniqueness, these turn out to be probabilistic strong solutions, as well. This is joint work with Luca Scarpa (Politecnico Milano).