Multi-valued, singular stochastic evolution inclusions
- Authors: Benjamin Gess, Jonas M. Tölle
- Preprint year: 2011
- First public date: 2011-12-23
- arXiv: 1112.5672
- Status: Published
- Publication type: Journal article
- Publication year: 2014
- Journal: Journal de mathématiques pures et appliquées, 101 (2014) 6, pp. 789-827
- DOI: 10.1016/j.matpur.2013.10.004
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.