Maximal dissipativity of Kolmogorov operators with Cahn–Hilliard type drift term

Abstract

We prove the existence of invariant measures μ for Kolmogorov operators L F associated with semilinear stochastic partial differential equations with Cahn–Hilliard type drift term. Based on gradient estimates on the pseudo-resolvent associated with L F and a priori estimates for the moments of μ we prove maximal dissipativity of L F in the space L 1 ( μ ) .