Schauder regularity results in separable Hilbert spaces

TL;DR

This paper establishes Schauder regularity estimates for solutions of certain stochastic partial differential equations in separable Hilbert spaces, advancing the understanding of their regularity properties.

Contribution

It provides new Schauder type estimates for solutions driven by weak generators of transition semigroups in infinite-dimensional Hilbert spaces.

Findings

Schauder estimates are extended to solutions of SPDEs in Hilbert spaces

Regularity results apply to both stationary and evolution equations

The work advances the theory of regularity for infinite-dimensional stochastic equations

Abstract

We prove Schauder type estimates for solutions of stationary and evolution equations driven by weak generators of transition semigroups associated to a semilinear stochastic partial differential equations with values in a separable Hilbert space.