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...
| Main Authors: | , |
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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 |
| Subjects: | |
| Online Access: | https://mathematicalanalysis.unibo.it/article/view/16154 |
| _version_ | 1797957035199823872 |
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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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