Reflected stochastic partial differential equations with fully local monotone coefficients in infinite dimensional domains

Abstract

This paper establishes the well-posedness of stochastic partial differential equations with reflection in an infinite-dimensional ball, within the fully local monotone framework. We prove a key variational inequality under convergence of weak topologies. Our result is very general, including many important models such as the stochastic Allen-Cahn equations, stochastic p-Laplacian equations, as well as more complex systems like the stochastic Cahn-Hilliard equations and the stochastic 3D tamed Navier-Stokes equations.

Theorems & Definitions (19)

• Definition 1.1
• Remark
• Lemma 3.1
• Theorem 3.2
• Lemma 3.3
• Lemma 3.4
• Lemma 3.5
• Theorem 4.1
• Lemma 4.2
• proof