Harnack inequalities for a class of semilinear stochastic partial differential equations

TL;DR

This paper establishes Harnack inequalities for a class of semilinear stochastic partial differential equations driven by space-time white noise, using coupling methods to demonstrate the strong Feller property and generalize previous results.

Contribution

It introduces new Harnack inequalities for semilinear SPDEs driven by white noise, extending prior work and applicable to reaction-diffusion and transport-diffusion equations.

Findings

Harnack inequalities proven for the class of SPDEs considered

Strong Feller property established for the associated semigroup

Results applicable to reaction-diffusion and transport-diffusion equations

Abstract

In this article, we study a class of semilinear stochastic partial differential equations driven by an additive space time white noise. We establish Harnack inequalities for the semigroup associated with the solution by using coupling method, which implies the strong Feller property. Our results generalize the results of Zhang [Potential Analysis 33 (2010), no. 2, 137-151.] and can be applied to some types of SPDE such as reaction-diffusion equation and transport-diffusion equation perturbed by space time white noise.