241536 Stochastic variational inequalities (V) (WiSe 2018/2019)

In this lecture series we will introduce the concept of stochastic variational inequalities (SVI) as a concept of solutions to SPDE. The interest in this concept of solutions is twofold: First, SVI solutions can be used in certain situations in which the "variational" approach to SPDE fails, e.g. multi-valued cases. We will demonstrate this by applying the general theory of SVI solutions to the stochastic total variation flow, arising in self-organized criticality. Second, the concept of SVI solutions offers nice stability properties with respect to perturbations, which will be demonstrated by introducing a stochastic analog of Mosco-convergence which yields a sufficient condition for the convergence of the corresponding semigroups. The general theory will be demonstrated by proving the convergence of non-local approximations to local stochastic p-Laplace equations.