Quasilinear stochastic elliptic equations with reflection: The existence of a density (Q1283375)

It is shown that the law of the solution of an elliptic stochastic partial differential equation with additive white noise reflected at zero is absolutely continuous with respect to Lebesgue measure. The proof requires the Malliavin calculus, some methods of variational inequalities and ordinary partial differential equations driven by measure data. Preliminary matter on these methods is provided.