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We consider the initial boundary value problem of non-homogeneous stochasticheat equation. The derivative of the solution with respect to time receivesheavy random perturbation. The space boundary is Lipschitz and we imposenon-zero cylinder condition. We prove a regularity result after findingsuitable spaces for the solution and the pre-assigned datum in the problem. Thetools from potential theory, harmonic analysis and probability are used. SomeLemmas are as important as the main Theorem.

On Initial-Boundary Value Problem of Stochastic Heat Equation in a Lipschitz Cylinder