Summary: We prove existence and uniqueness of strong solutions for a class of second-order stochastic PDEs with multiplicative Wiener noise and drift of the form \({\operatorname{div}}\gamma (\nabla \cdot )\), where \(\gamma \) is a maximal monotone graph in \(\mathbb {R}^n \times \mathbb {R}^n\) obtained as the subdifferential of a convex function satisfying very mild assumptions on its behavior at infinity. The well-posedness result complements the corresponding one in our recent work [the authors, “Strong solutions to SPDEs with monotone drift in divergence form”, Preprint, arXiv:1612.08260] where, under the additional assumption that \(\gamma \) is single-valued, a solution with better integrability and regularity properties is constructed. The proof given here, however, is self-contained.
For the entire collection see [Zbl 1402.35005].