Ergodicity and Kolmogorov equations for dissipative SPDEs with singular drift: a variational approach

Abstract

We prove existence of invariant measures for the Markovian semigroup generated by the solution to a parabolic semilinear stochastic PDE whose nonlinear drift term satisfies only a kind of symmetry condition on its behavior at infinity, but no restriction on its growth rate is imposed. Thanks to strong integrability properties of invariant measures $\mu$, solvability of the associated Kolmogorov equation in $L^1(\mu )$ is then established, and the infinitesimal generator of the transition semigroup is identified as the closure of the Kolmogorov operator. A key role is played by a generalized variational setting.

32 pages

References in corpus (1)

• A variational approach to dissipative SPDEs with singular drift

Cited by in corpus (4)

• On the stochastic Cahn-Hilliard equation with a singular double-well potential
• Doubly nonlinear stochastic evolution equations
• Refined existence and regularity results for a class of semilinear dissipative SPDEs
• Deterministic Control of Stochastic Reaction-Diffusion Equations