Smoothing effects and maximal H\"older regularity for non-autonomous Kolmogorov equations in infinite dimension

TL;DR

This paper establishes smoothing effects and optimal regularity estimates for nonautonomous Kolmogorov equations in infinite-dimensional spaces, driven by time-dependent Ornstein-Uhlenbeck operators, relevant for stochastic differential equations with Gaussian noise.

Contribution

It provides the first comprehensive analysis of regularity and smoothing properties for nonautonomous infinite-dimensional Kolmogorov equations with explicit Schauder estimates.

Findings

Proved smoothing properties for the class of equations.

Derived optimal Schauder type regularity estimates.

Applicable to stochastic differential equations with Gaussian noise.

Abstract

We prove smoothing properties and optimal Schauder type estimates for a class of nonautonomous evolution equations driven by time dependent Ornstein-Uhlenbeck operators in a separable Hilbert space. They arise as Kolmogorov equations of linear nonautonomous stochastic differential equations with Gaussian noise.