On Initial-Boundary Value Problem of the Stochastic Heat Equation in Lipschitz Cylinders

Tongkeun Chang (), Kijung Lee () and Minsuk Yang ()
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Tongkeun Chang: Yonsei University
Kijung Lee: Ajou University
Minsuk Yang: Yonsei University

Journal of Theoretical Probability, 2013, vol. 26, issue 4, 1135-1164

Abstract: Abstract We consider the initial boundary value problem of the non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random noises. The space boundary is Lipschitz, and we impose nonzero condition on the parabolic boundary. We prove a regularity result by finding appropriate spaces for solutions and pre-assigned data in the problem. We use a collection of tools from potential theory, harmonic analysis, and probability. Some lemmas are as important as the main theorem.

Keywords: Stochastic heat equation; Lipschitz cylinders; Initial-boundary value problem; Anisotropic Besov space; 60H15; 35R60 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-012-0444-1

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