Harnack inequalities for a class of semilinear stochastic partial differential 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.

I am not satisfied with the current result