Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation. (Q1426659)

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.