SPDEs with non-Lipschitz coefficients and nonhomogeneous boundary conditions

In this article, we consider a stochastic partial differential equation (SPDE) driven by Gaussian colored noise with Dirichlet, Neumann or mixed nonhomogeneous random boundary conditions when the drift and diffusion coefficients are non-Lipschitz. We prove the existence of a unique strong solution to this SPDE and obtain a comparison theorem between such SPDEs. We also study the Holder continuity of the solution in both time and space variables, and find the dependence of the Holder exponent on that of the Dirichlet boundary.