A basis of resolutive sets for the heat equation: an elementary construction
By an easy “trick” taken from the caloric polynomial theory, we prove the existence of a basis of the Euclidean topology whose elements are resolutive sets of the heat equation. This result can be used to construct, with a very elementary approach, the Perron solution of the caloric Dirichlet proble...
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Format: | Article |
Language: | English |
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University of Bologna
2023-01-01
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Series: | Bruno Pini Mathematical Analysis Seminar |
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Online Access: | https://mathematicalanalysis.unibo.it/article/view/16154 |
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author | Alessia E. Kogoj Ermanno Lanconelli |
author_facet | Alessia E. Kogoj Ermanno Lanconelli |
author_sort | Alessia E. Kogoj |
collection | DOAJ |
description | By an easy “trick” taken from the caloric polynomial theory, we prove the existence of a basis of the Euclidean topology whose elements are resolutive sets of the heat equation. This result can be used to construct, with a very elementary approach, the Perron solution of the caloric Dirichlet problem on arbitrary bounded open subsets of the Euclidean space-time. |
first_indexed | 2024-04-10T23:59:07Z |
format | Article |
id | doaj.art-9b82a33faf5e4ee0a21191e13bf18faf |
institution | Directory Open Access Journal |
issn | 2240-2829 |
language | English |
last_indexed | 2024-04-10T23:59:07Z |
publishDate | 2023-01-01 |
publisher | University of Bologna |
record_format | Article |
series | Bruno Pini Mathematical Analysis Seminar |
spelling | doaj.art-9b82a33faf5e4ee0a21191e13bf18faf2023-01-10T08:50:39ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292023-01-011311810.6092/issn.2240-2829/1615414504A basis of resolutive sets for the heat equation: an elementary constructionAlessia E. Kogoj0Ermanno Lanconelli1Università di UrbinoUniversità di BolognaBy an easy “trick” taken from the caloric polynomial theory, we prove the existence of a basis of the Euclidean topology whose elements are resolutive sets of the heat equation. This result can be used to construct, with a very elementary approach, the Perron solution of the caloric Dirichlet problem on arbitrary bounded open subsets of the Euclidean space-time.https://mathematicalanalysis.unibo.it/article/view/16154heat equationcaloric dirichlet problemperron solutionpotential analysis |
spellingShingle | Alessia E. Kogoj Ermanno Lanconelli A basis of resolutive sets for the heat equation: an elementary construction Bruno Pini Mathematical Analysis Seminar heat equation caloric dirichlet problem perron solution potential analysis |
title | A basis of resolutive sets for the heat equation: an elementary construction |
title_full | A basis of resolutive sets for the heat equation: an elementary construction |
title_fullStr | A basis of resolutive sets for the heat equation: an elementary construction |
title_full_unstemmed | A basis of resolutive sets for the heat equation: an elementary construction |
title_short | A basis of resolutive sets for the heat equation: an elementary construction |
title_sort | basis of resolutive sets for the heat equation an elementary construction |
topic | heat equation caloric dirichlet problem perron solution potential analysis |
url | https://mathematicalanalysis.unibo.it/article/view/16154 |
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