Existence of the Fomin derivative of the invariant measure of a stochastic reaction-diffusion equation (Mathematical Analysis of Viscous Incompressible Fluid)
Giuseppe Da Prato, Arnaud Debussche · Institutional Repositories DataBase (IRDB) · 2015
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 $\Vert\varphi\Vert_{L^{2}(H, u)}$ , where $ u$ is the invariant measure of $P_{t}.$2010