Multi-valued, singular stochastic evolution inclusions

Benjamin Gess*, Jonas M. Tölle

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)

Abstract

We provide an abstract variational existence and uniqueness result for multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert spaces with general additive and Wiener multiplicative noise. As examples we discuss certain singular diffusion equations such as the stochastic 1-Laplacian evolution (total variation flow) in all space dimensions and the stochastic singular fast-diffusion equation. In case of additive Wiener noise we prove the existence of a unique weak*-mean ergodic invariant measure.

Original languageEnglish
Pages (from-to)789-827
Number of pages39
JournalJOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume101
Issue number6
DOIs
Publication statusPublished - 2014
MoE publication typeA1 Journal article-refereed

Keywords

  • Ergodic semigroup
  • Logarithmic diffusion
  • p-Laplacian equation
  • Singular stochastic evolution equation

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