# Schauder theorems for Ornstein-Uhlenbeck equations in infinite dimension

## TL;DR

This paper establishes Schauder estimates for Ornstein-Uhlenbeck equations in infinite-dimensional Banach spaces with Gaussian measures, advancing the understanding of regularity for such stochastic PDEs.

## Contribution

It provides the first Schauder estimates for Ornstein-Uhlenbeck equations in infinite-dimensional Banach spaces, extending classical finite-dimensional results.

## Key findings

- Schauder estimates are proved for stationary Ornstein-Uhlenbeck equations.
- Schauder estimates are proved for evolution Ornstein-Uhlenbeck equations.
- Results apply to equations driven by classical Ornstein-Uhlenbeck operators in Banach spaces.

## Abstract

We prove Schauder type estimates for stationary and evolution equations driven by the classical Ornstein-Uhlenbeck operator in a separable Banach space, endowed with a centered Gaussian measure.