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

Boundary Value Problems volume 2005, Article number: 289712 (2005) Cite this article

Abstract

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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  1. Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL, 32901, USA
    • Ugur G Abdulla
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  1. Ugur G Abdulla
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Correspondence to Ugur G Abdulla.

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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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