  We mainly investigate the log-Harnack inequality for the reflected stochastic
partial differential equation driven by multiplicative noises based on the
gradient estimate of the associated Markov semigroup. To do it, the
penalization method and the comparison principle for stochastic partial
differential equations are adopted. As its applications, we also establish the
entropy-cost inequality and study some important estimates of the transition
density relative to its invariant measure.
