Variational methods for doubly nonlinear stochastic evolution equations

We give an overview of some recent results for doubly nonlinear stochastic evolution equations in Hilbert spaces. In the first part of the talk we introduce the prototypes of the problems in consideration and we discuss the main existence results. Secondly, we provide alternative proofs of existence which rely on convex minimisation techniques, such as the Weighted-Energy-Dissipation (WED) and the Energy-Dissipation principles (EDP). Eventually, we discuss some current open problems, focusing above all on the direction of uniqueness-by-noise for doubly nonlinear evolutions.
The works presented in the talk are based on joint collaborations with Prof. Ulisse Stefanelli (University of Vienna, Austria).


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