A NOTE ON REGULARITY AND SEPARATION FOR THE STOCHASTIC ALLEN-CAHN EQUATION WITH LOGARITHMIC POTENTIAL

We prove refined space-time regularity for the classical stochastic Allen-Cahn equation with logarithmic potential. This allows to establish a random separation property, i.e. that the trajectories of the solution are strictly separated from the potential barriers. The present contribution extends the results obtained in [2], where separation was proved only for p-Laplace operators with p greater than the space-dimension.