Existence of strong solutions for stochastic porous media equation under general monotonicity conditions

This paper addresses the existence and uniqueness of strong solutions to stochastic porous media equations dX - (X) dt = B(X) dW(t) in bounded domains of Rd with Dirichlet boundary conditions. Here - is a maximal monotone graph in R × R (possibly multivalued) with the domain and range all of R. Compared with the existing literature on stochastic porous media equations, no growth condition on - is assumed and the diffusion coefficient - might be multivalued and discontinuous. The latter case is encountered in stochastic models for self-organized criticality or phase transition.