Section: New Results

Existence of the Fomin derivative of the invariant measure of a stochastic reaction-diffusion equation

In [48] , we consider a reaction-diffusion equation perturbed by noise (not necessarily white). We prove existence of the Fomin derivative of the corresponding transition semigroup $P_t$. The main tool is a new estimate for $P_{t}D\varphi$ in terms of ${\parallel \varphi \parallel }_{L^2(H,\nu )}$, where $\nu$ is the invariant measure of $P_t$.