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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)
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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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