A note on doubly nonlinear SPDEs with singular drift in divergence form

Abstract

We prove well-posedness for a class of second-order SPDEs with multiplicative Wiener noise and doubly nonlinear drift of the form –div $\gamma (\nabla \cdot )+\beta (\cdot )$, where $\gamma$ is the subdifferential of a convex function on ${\mathbb{R}}^d$ and $\beta$ is a maximal monotone graph everywhere defined on $\mathbb{R}$, on which neither growth nor continuity assumptions are imposed.