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 |
| _version_ | 1811285506790522880 |
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| author | Ugur G. Abdulla |
| author_facet | Ugur G. Abdulla |
| author_sort | Ugur G. Abdulla |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T02:45:12Z |
| format | Article |
| id | doaj.art-8df1b3f40d8c41e8885c4c85aa285cad |
| institution | Directory Open Access Journal |
| issn | 1687-2762 1687-2770 |
| language | English |
| last_indexed | 2024-04-13T02:45:12Z |
| publishDate | 2005-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-8df1b3f40d8c41e8885c4c85aa285cad2022-12-22T03:06:03ZengSpringerOpenBoundary Value Problems1687-27621687-27702005-06-012005218119910.1155/BVP.2005.181Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equationUgur G. AbdullaThis 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.http://dx.doi.org/10.1155/BVP.2005.181 |
| spellingShingle | Ugur G. Abdulla Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation Boundary Value Problems |
| title | Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation |
| title_full | Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation |
| title_fullStr | Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation |
| title_full_unstemmed | Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation |
| title_short | Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation |
| title_sort | multidimensional kolmogorov petrovsky test for the boundary regularity and irregularity of solutions to the heat equation |
| url | http://dx.doi.org/10.1155/BVP.2005.181 |
| work_keys_str_mv | AT ugurgabdulla multidimensionalkolmogorovpetrovskytestfortheboundaryregularityandirregularityofsolutionstotheheatequation |