Multi-valued, singular stochastic evolution inclusions

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.

39 pages, in press: J. Math. Pures Appl. (2013)

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Cited by in corpus (20)

• Entropy solutions for stochastic porous media equations
• Stability of solutions to stochastic partial differential equations
• Finite time extinction for stochastic sign fast diffusion and self-organized criticality
• Ergodicity and local limits for stochastic local and nonlocal p-Laplace equations
• Nonlinear diffusion equations with nonlinear gradient noise
• Convergence of invariant measures for singular stochastic diffusion equations
• Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise
• A gradient flow formulation for the stochastic Amari neural field model
• Ergodicity for Stochastic Porous Media Equations
• Corrigendum to `Convergence of invariant measures for singular stochastic diffusion equations'
• Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions
• Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations
• The total variation flow perturbed by gradient linear multiplicative noise
• Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations
• Ergodicity for singular-degenerate porous media equations
• Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organised criticality
• Improved regularity for the stochastic fast diffusion equation
• On Young regimes for locally monotone SPDEs
• Stability and moment estimates for the stochastic singular $\Phi$-Laplace equation
• Singular-degenerate multivalued stochastic fast diffusion equations