A priori estimates of invariant measures for semilinear SPDE's and applications

We study existence and a priori estimates of invariant measures $\mu$ for a class of semilinear stochastic differential equation with additive noise on a separable Hilbert space. Furthermore, we discuss the corresponding parabolic Cauchy-problem in $L^1(mu)$. Particular emphasis will be put on stochastic reaction diffusion, and Cahn-Hilliard equations.