Nonlinear stochastic Laplace equation: Large Deviations and Measure Concentration

TL;DR

This paper establishes a large deviation principle and measure concentration for solutions of the stochastic p-Laplace equation driven by Brownian noise, using advanced probabilistic and analytical techniques.

Contribution

It introduces a novel large deviation principle and measure concentration results for the stochastic p-Laplace equation on unbounded domains, employing the weak convergence and Girsanov transformation methods.

Findings

Large deviation principle for the strong solution established.

Quadratic transportation cost inequality proved.

Measure concentration phenomenon demonstrated.

Abstract

In this paper, a large deviation principle for the strong solution of the p-Laplace equation on unbounded domain driven by small multiplicative Brownian noise is established. The weak convergence approach and the localized time increment estimate plays a crucial role to establish the large deviation principle. Moreover, based on the Girsanov transformation and the standard L2-uniqueness approach, the quadratic transportation cost information inequality is proved for the strong solution to the underlying problem which then implies the measure concentration phenomenon.