Invariance of subspaces under the solution flow of SPDE

In this paper we investigate some regularity property for the solution to SPDE. Under certain assumptions we prove that the solution of an SPDE takes values in some subspace of the original state space if the initial condition does. As examples, the main results are applied to different types of SPDE such as stochastic reaction-diffusion equations, the stochastic p-Laplace equation, stochastic porous media and fast diffusion equations in Hilbert space. AMS subject Classification: 60H1