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 language | English |
|---|---|
| Pages (from-to) | 789-827 |
| Number of pages | 39 |
| Journal | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES |
| Volume | 101 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2014 |
| MoE publication type | A1 Journal article-refereed |
Keywords
- Ergodic semigroup
- Logarithmic diffusion
- p-Laplacian equation
- Singular stochastic evolution equation
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Cite this
Gess, B., & Tölle, J. M. (2014). Multi-valued, singular stochastic evolution inclusions. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 101(6), 789-827. https://doi.org/10.1016/j.matpur.2013.10.004