Large deviations for a stochastic Cahn-Hilliard equation in H\"older norm

TL;DR

This paper establishes a Large Deviations Principle for solutions of a stochastic Cahn-Hilliard equation driven by space-time white noise, using a weak convergence approach in the H"older norm.

Contribution

It introduces a novel application of the weak convergence method to prove LDP for stochastic PDEs in H"older spaces.

Findings

LDP is proven for the stochastic Cahn-Hilliard equation in H"older norm.

The weak convergence approach simplifies the proof by focusing on controlled analogues.

The results extend large deviations theory to complex stochastic PDEs with space-time white noise.

Abstract

We consider a stochastic Cahn-Hilliard partial differential equation driven by a space-time white noise. We prove the Large Deviations Principle (LDP) for the law of the solutions in the H\"older norm. We use the weak convergence approach that reduces the proof to establishing basic qualitative properties for controlled analogues of the original stochastic system.