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 Σ 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 Σ.
"Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space." Ann. Probab. 37 (4) 1427 - 1458, July 2009. https://doi.org/10.1214/08-AOP438