  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
$\Sigma$.
