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

We prove the existence of invariant measures μ for Kolmogorov operators LF associated with semilinear stochastic partial differential equations with Cahn–Hilliard type drift term. Based on gradient estimates on the pseudo-resolvent associated with LF and a priori estimates for the moments of μ we prove maximal dissipativity of LF in the space L1(μ).