Da Prato, Giuseppe and Debussche, Arnaud and Tubaro, Luciano (2003) Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation. UNSPECIFIED. (Unpublished)
We prove essential self-adjointness of Kolmogorov operators corresponding to gradient systems with potentials U such that DU is not square integrable with respect the invariant measure (irregular potentials). An application is given to the Cahn-Hilliard-Cook equation in dimension one. In this case the spectral gap is proved for the correspondig semigroup. We also obtain a log-Sobolev inequality.
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