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Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation. (English) Zbl 1038.60055
The authors are concerned with a Kolmogorov operator corresponding to gradient systems with a semi-convex potential $$U$$ such that $$DU$$ is not square integrable with respect to the invariant measure. This setting is suited to the study of the stochastic Cahn-Hilliard equation in the interval $$[0,\pi]$$. In this case the Kolmogorov operator is essentially self-adjoint, and Poincaré and log-Sobolev inequalities hold for the invariant measure. This implies a spectral gap property for the closure of the operator.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis)
##### Keywords:
stochastic Cahn-Hilliard equation; Kolmogorov operator
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