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

Ugur G. Abdulla | Zendy

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

Author(s) -

Ugur G. Abdulla

Publication year - 2005

Publication title -

boundary value problems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.579

H-Index - 38

eISSN - 1687-2770

pISSN - 1687-2762

DOI - 10.1155/bvp.2005.181

Subject(s) - mathematics , heat equation , brownian motion , partial differential equation , mathematical analysis , ordinary differential equation , boundary (topology) , diffusion , point (geometry) , boundary value problem , differential equation , statistics , geometry , physics , thermodynamics

This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset of Ã¢Â„ÂN+1 (NÃ¢Â‰Â¥2) for the diffusion (or heat) equation. The result implies asymptotic probability law for the standard N-dimensional Brownian motion

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