On the Solution of the Exterior Dirichlet Problem for an Axisymmetric Potential
For an unbounded domain of the meridian plane with bounded smooth boundary that satisfies certain additional conditions, we develop a method for the reduction of the Dirichlet problem for an axisymmetric potential to Fredholm integral equations. In the case where the boundary of the domain is a unit...
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| Date: | 2002 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4202 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510332411183104 |
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| author | Plaksa, S. A. Плакса, С. А. Плакса, С. А. |
| author_facet | Plaksa, S. A. Плакса, С. А. Плакса, С. А. |
| author_sort | Plaksa, S. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:24:06Z |
| description | For an unbounded domain of the meridian plane with bounded smooth boundary that satisfies certain additional conditions, we develop a method for the reduction of the Dirichlet problem for an axisymmetric potential to Fredholm integral equations. In the case where the boundary of the domain is a unit circle, we obtain a solution of the exterior Dirichlet problem in explicit form. |
| first_indexed | 2026-03-24T02:55:19Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4202 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:55:19Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/2b/817e917c02fec246100e5452e8acb42b.pdf |
| spelling | umjimathkievua-article-42022020-03-18T20:24:06Z On the Solution of the Exterior Dirichlet Problem for an Axisymmetric Potential К решению внешней задачи Дирихле для осесимметричного потенциала Plaksa, S. A. Плакса, С. А. Плакса, С. А. For an unbounded domain of the meridian plane with bounded smooth boundary that satisfies certain additional conditions, we develop a method for the reduction of the Dirichlet problem for an axisymmetric potential to Fredholm integral equations. In the case where the boundary of the domain is a unit circle, we obtain a solution of the exterior Dirichlet problem in explicit form. Для необмеженої област і меридіанної площини з обмеженою гладкою межею, що задовольняє деякі додаткові умови, розроблено метол редукції задачі Діріхле для осесиметричпої о потенціалу до інтегральних рівнянь Фредгольма. У випадку, коли межею області є одиничне коло, розв'язок зовнішньої задачі Діріхле одержано в явному вигляді. Institute of Mathematics, NAS of Ukraine 2002-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4202 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 12 (2002); 1634-1641 Український математичний журнал; Том 54 № 12 (2002); 1634-1641 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4202/5111 https://umj.imath.kiev.ua/index.php/umj/article/view/4202/5112 Copyright (c) 2002 Plaksa S. A. |
| spellingShingle | Plaksa, S. A. Плакса, С. А. Плакса, С. А. On the Solution of the Exterior Dirichlet Problem for an Axisymmetric Potential |
| title | On the Solution of the Exterior Dirichlet Problem for an Axisymmetric Potential |
| title_alt | К решению внешней задачи Дирихле для осесимметричного потенциала |
| title_full | On the Solution of the Exterior Dirichlet Problem for an Axisymmetric Potential |
| title_fullStr | On the Solution of the Exterior Dirichlet Problem for an Axisymmetric Potential |
| title_full_unstemmed | On the Solution of the Exterior Dirichlet Problem for an Axisymmetric Potential |
| title_short | On the Solution of the Exterior Dirichlet Problem for an Axisymmetric Potential |
| title_sort | on the solution of the exterior dirichlet problem for an axisymmetric potential |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4202 |
| work_keys_str_mv | AT plaksasa onthesolutionoftheexteriordirichletproblemforanaxisymmetricpotential AT plaksasa onthesolutionoftheexteriordirichletproblemforanaxisymmetricpotential AT plaksasa onthesolutionoftheexteriordirichletproblemforanaxisymmetricpotential AT plaksasa krešeniûvnešnejzadačidirihledlâosesimmetričnogopotenciala AT plaksasa krešeniûvnešnejzadačidirihledlâosesimmetričnogopotenciala AT plaksasa krešeniûvnešnejzadačidirihledlâosesimmetričnogopotenciala |