Convergence of invariant measures for singular stochastic diffusion equations

It is proved that the solutions to the singular stochastic p-Laplace equation, p∈(1,2) and the solutions to the stochastic fast diffusion equation with nonlinearity parameter r∈(0,1) on a bounded open domain Λ⊂R^d with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters p and r respectively (in the Hilbert spaces L²(Λ), H^-1(Λ) respectively). The highly singular limit case p=1 is treated with the help of stochastic evolution variational inequalities, where P-a.s. convergence, uniformly in time, is established. It is shown that the associated unique invariant measures of the ergodic semigroups converge in the weak sense (of probability measures).