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Multi-valued, singular stochastic evolution inclusions. (English) Zbl 1295.47042

General existence and uniqueness results of variational solutions are derived for multi-valued, monotone, non-coercive stochastic inclusions with general additive noise or multiplicative Wiener noise. The main results are applied to specific models including the stochastic \(p\)-Laplacian equation with \(p\in [1,2)\) (note that the case \(p\geq 2\) is easier to treat and has been well studied in the literature). Ergodicity of the associated Markov semigroup is also studied for the Wiener noise case.

MSC:

47D07 Markov semigroups and applications to diffusion processes
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
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