Absolute Continuity of Solutions to Reaction-Diffusion Equations with Multiplicative Noise

Abstract We prove absolute continuity of the law solution, evaluated at fixed points in time and space, to a parabolic dissipative stochastic PDE on L 2 ( G ), where is an open bounded domain $\mathbb {R}^{d}$ ℝ d with smooth boundary. The equation driven by multiplicative Wiener noise nonlinear drift term superposition operator associated real function that assumed be monotone, locally Lipschitz continuous, growing not faster than polynomial. proof, which uses arguments Malliavin calculus, crucially relies well-posedness theory mild sense for evolution equations Banach spaces.