Wang's Harnack inequalities for space-time white noises driven SPDEs with two reflecting walls and their applications

In this paper, we establish Wang's Harnack inequalities for Gaussian space-time white noises driven the stochastic partial differential equation with double reflecting walls, which is of the infinite dimensional Skorokhod equation. We first establish both the Harnack inequality with power and the log-Harnack inequality for the special case of additive noises by the coupling approach. Then we investigate the log-Harnack inequality for the Markov semigroup associated with the reflected SPDE driven by multiplicative noises using the penalization method and the comparison principle for SPDEs. As their applications, we study the strong Feller property, uniqueness of invariant measures, the entropy-cost inequality, and some other important properties of the transition density.