Kolmogorov Equation Associated to the Stochastic Reflection Problem on a Smooth Convex Set of a Hilbert Space

Here A :D(A) ⊂H →H is a self-adjoint operator, K = {x ∈H :g(x) ≤ 1}, where g :H → R is convex and of class C∞, NK(x) is the normal cone to K at x and W (t) is a cylindrical Wiener process in H (see Hypothesis 1.1 for more precise assumptions). Obviously the expression in (1.1) is formal and its precise meaning should be defined. When H is finite-dimensional a solution to (1.1) is a pair of continuous adapted processes (X,η) such that X is K-valued, η is of bounded variation with dη concentrated on the set of times where X(t) ∈ Σ (the boundary of K) and