  We consider an elliptic Kolmogorov equation lambda u - Ku =f in a convex
subset C of a separable Hilbert space X. We prove maximal Sobolev regularity of
its weak solution, when lambda >0 and f is in L^2(C,nu), where nu is the
log-concave measure associated to the system. Moreover we prove maximal
estimates on the gradient of u, that allow to show that u satisfies the Neumann
boundary condition in the sense of traces at the boundary of C. The general
results are applied to Kolmogorov equations of reaction-diffusion stochastic
PDEs and Cahn-Hilliard stochastic PDEs in convex sets of suitable Hilbert
spaces.
