Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space

We consider the stochastic reflection problem associated with a self-adjoint operator $A$ and a cylindrical Wiener process on a convex set $K$ with nonempty interior and regular boundary $\Sigma$ in a Hilbert space $H$. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on $\Sigma$.
Comment: Published in at http://dx.doi.org/10.1214/08-AOP438 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)