Hypercontractivity for space-time white noise driven SPDEs with reflection

The hypercontractive property of the Markov semigroup associated with the reflected stochastic partial differential equation driven by the additive space-time white noise is mainly investigated. The main tool for its proof is the general criterion presented recently by F.-Y. Wang [29]. In particular, we obtain the hyperboundedness and the compactness of the Markov semigroup, the exponential convergences of the entropy, the exponential convergences of the Markov semigroup to its unique invariant measure in both L-2 and the total variation norm. (C) 2018 Elsevier Inc. All rights reserved.