| Abstract: |
| We are mainly interested in the dimension-free Harnack inequalities for the stochastic partial differential equation with reflecting walls. The reflected SPDE is one kind of one kind of random obstacle problems and is usually regarded as the infinite-dimensional Skorokhod problem. We first establish the Harnack inequalities for the reflected SPDE and then apply them to the study of various properties of Markov semigroup associated with the reflected SPDE, for example, the uniqueness of invariant measures, the entropy-cost inequality and Hyperboundedness. |
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