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arXiv · 1106.6125

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

Tongkeun Chang·Kijung Lee·Minsuk Yang
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Abstract

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.

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Tongkeun Chang, Kijung Lee, Minsuk Yang. 2011-06-30. On Initial-Boundary Value Problem of Stochastic Heat Equation in a Lipschitz Cylinder. https://arxiv.org/abs/1106.6125

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