Stochastic partial differential equations

Head:
Benjamin Gess (Email, Homepage)

Phone:
+49 (0) 341 - 9959 - 954

Fax:
+49 (0) 341 - 9959 - 585

Address:
Inselstr. 22
04103 Leipzig

Summerterm 2019

Stochastic variational inequalities

  • Lecturer: Benjamin Gess
  • Date: Monday 16:15 - 17:45
  • Room: MPI MiS, A3 01
  • Language: English
  • Target audience: MSc students, PhD students, Postdocs
  • Prerequisites: functional analysis, basic convex analysis

Abstract

In this lecture series we will introduce the concept of stochastic variational inequalities (SVI) as a concept of solutions to SPDE. Our interest in this concept of solutions comes from two directions: First, SVI solutions can be used in certain situations in which the "variational" approach to SPDE fails, e.g. for multi-valued SPDE. We will encounter this in the application to the stochastic total variation flow, with links to 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. This yields a sufficient condition for the convergence of the corresponding solutions to SPDE. The general theory will be laid out by proving the convergence of non-local approximations to local stochastic p-Laplace equations.

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28.03.2019, 10:40