Schauder estimates for some perturbation of an infinite dimensional Ornstein-Uhlenbeck operator (Q1942791)

The author introduces a semilinear elliptic problem in which the leading, linear term is an infinite-dimensional Ornstein-Uhlenbeck-type operator and the nonlinear perturbation satisfies a smoothness assumption (more precisely, it has to be given by a Hilbert-space-valued function that is uniformly continuous and bounded together with its derivatives up to order 3). If the drift term is given by a negative definite operator with trace-class inverse, then the solution to the associated elliptic problem is shown to satisfy some Schauder-type a-priori estimates.