On Initial-Boundary Value Problem of Stochastic Heat Equation in a   Lipschitz Cylinder
  We consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero cylinder condition. We prove a regularity result after finding suitable spaces for the solution and the pre-assigned datum in the problem. The tools from potential theory, harmonic analysis and probability are used. Some Lemmas are as important as the main Theorem. 
Tongkeun Chang, Kijung Lee and Minsuk Yang
math.AP