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.