Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem
Elliptic systems of two second-order equations, which can be written as a single equation with complex coefficients and a homogeneous operator, are studied. The necessary and sufficient conditions for the connection of traces of a solution are obtained for an arbitrary bounded domain with a smooth b...
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| Datum: | 1993 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5954 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512178622169088 |
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| author | Burskii, V. P. Бурский, В. П. Бурский, В. П. |
| author_facet | Burskii, V. P. Бурский, В. П. Бурский, В. П. |
| author_sort | Burskii, V. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:21:58Z |
| description | Elliptic systems of two second-order equations, which can be written as a single equation with complex coefficients and a homogeneous operator, are studied. The necessary and sufficient conditions for the connection of traces of a solution are obtained for an arbitrary bounded domain with a smooth boundary. These conditions are formulated in the form of a certain moment problem on the boundary of a domain; they are applied to the study of boundary-value problems. In particular, it is shown that the Dirichlet problem and the Neumann problem are solvable only together. In the case where the domain is a disk, the indicated moment problem is solved together with the Dirichlet problem and the Neumann problem. The third boundary-value problem in a disk is also investigated. |
| first_indexed | 2026-03-24T03:24:40Z |
| format | Article |
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| id | umjimathkievua-article-5954 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:24:40Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/90/23855f45dbda32b5cc3cb8be12ec9990.pdf |
| spelling | umjimathkievua-article-59542020-03-19T09:21:58Z Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem О краевых задачах для эллиптического уравнения с комплексными коэффициекгами и одной проблеме моментов Burskii, V. P. Бурский, В. П. Бурский, В. П. Elliptic systems of two second-order equations, which can be written as a single equation with complex coefficients and a homogeneous operator, are studied. The necessary and sufficient conditions for the connection of traces of a solution are obtained for an arbitrary bounded domain with a smooth boundary. These conditions are formulated in the form of a certain moment problem on the boundary of a domain; they are applied to the study of boundary-value problems. In particular, it is shown that the Dirichlet problem and the Neumann problem are solvable only together. In the case where the domain is a disk, the indicated moment problem is solved together with the Dirichlet problem and the Neumann problem. The third boundary-value problem in a disk is also investigated. Вивчаються еліптичні системи двох рівнянь другого порядку, які можна записати у вигляді одного рівняння з комплексними коефіцієнтами та однорідним оператором. У довільній обмеженій області з гладкою межею одержані необхідні та достатні умови зв'язку слідів розв'язку, які записані у вигляді однієї проблеми моментів на межі області і застосовуються до вивчення крайових задач. Показано, зокрема, що задачі Діріхле і Неймана лише одночасно розв’язуються. У випадку кола розв'язується сформульована проблема моментів, а з нею і задачі Діріхле та Неймана. Розглянуто також третю крайову задачу в колі. Institute of Mathematics, NAS of Ukraine 1993-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5954 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 11 (1993); 1476–1483 Український математичний журнал; Том 45 № 11 (1993); 1476–1483 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5954/8591 https://umj.imath.kiev.ua/index.php/umj/article/view/5954/8592 Copyright (c) 1993 Burskii V. P. |
| spellingShingle | Burskii, V. P. Бурский, В. П. Бурский, В. П. Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem |
| title | Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem |
| title_alt | О краевых задачах для эллиптического уравнения с комплексными коэффициекгами и одной проблеме моментов |
| title_full | Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem |
| title_fullStr | Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem |
| title_full_unstemmed | Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem |
| title_short | Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem |
| title_sort | boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5954 |
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