Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation
This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset of â„ÂN+1 (N≥2) for the diffusion (or heat) equation. The result implies asymptotic probability law for the standard N-dimensional Brownian motion....
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| Format: | Article |
| Language: | English |
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SpringerOpen
2005-06-01
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| Series: | Boundary Value Problems |
| Online Access: | http://dx.doi.org/10.1155/BVP.2005.181 |
| Summary: | This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset of â„ÂN+1 (N≥2) for the diffusion (or heat) equation. The result implies asymptotic probability law for the standard N-dimensional Brownian motion. |
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| ISSN: | 1687-2762 1687-2770 |