Large deviations for an obstacle problem with T-monotone operator and multiplicative noise

TL;DR

This paper establishes a large deviation principle for obstacle problems involving T-monotone operators and multiplicative noise, combining new conditions and inequalities to handle the stochastic and obstacle constraints.

Contribution

It introduces a novel approach combining recent sufficient conditions and Lewy-Stampacchia inequalities to prove LDP for complex obstacle problems with stochastic elements.

Findings

Established LDP for obstacle problems with T-monotone operators

Developed new methods to handle stochastic reaction and obstacle constraints

Extended large deviation theory to a new class of stochastic PDEs

Abstract

In this paper, we study the large deviation principle (LDP) for obstacle problems governed by a T-monotone operator and small multiplicative stochastic reaction. Our approach relies on a combination of new sufficient condition to prove LDP by Matoussi, Sabbagh and Zhang [Appl. Math. Optim. 2021] and Lewy-Stampacchia inequalities to manage the Lagrange-multiplier associated with the obstacle.