On the stochastic p-Laplace equation

The p-Laplace equation with random perturbation is studied for the singular case 1 < p ⩽ 2 in this paper. Some properties of the invariant measure and transition semigroups are obtained. The main tool is the dimension-free Harnack inequality, which is established by using the coupling argument. As consequences, some ergodicity, compactness and contractive properties are derived for the associated transition semigroups. The main results are applied to stochastic reaction–diffusion equations and the stochastic p-Laplace equation in Hilbert space.