Non-monotone stochastic generalized porous media equations

By using the Nash inequality and a monotonicity approximation argument, existence and uniqueness of strong solutions are proved for a class of non-monotone stochastic generalized porous media equations. Moreover, we prove for a large class of stochastic PDE that the solutions stay in the smaller L2-space provided the initial value does, so that some recent results in the literature are considerably strengthened.