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Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation

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This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset of () for the diffusion (or heat) equation. The result implies asymptotic probability law for the standard-dimensional Brownian motion.

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Correspondence to Ugur G Abdulla.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abdulla, U.G. Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation. Bound Value Probl 2005, 289712 (2005). https://doi.org/10.1155/BVP.2005.181

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  • DOI: https://doi.org/10.1155/BVP.2005.181