On the Sobolev problem in the complete scale of Banach spaces
In a bounded domainG with boundary ∂G that consists of components of different dimensions, we consider an elliptic boundary-value problem in complete scales of Banach spaces. The orders of boundary expressions are arbitrary; they are pseudodifferential along ∂G. We prove the theorem on a complete se...
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| Date: | 1999 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1999
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4714 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510877659168768 |
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| author | Los’, V. M. Roitberg, Ya. A. Лось, В. М. Ройтберг, Я. А. Лось, В. М. Ройтберг, Я. А. |
| author_facet | Los’, V. M. Roitberg, Ya. A. Лось, В. М. Ройтберг, Я. А. Лось, В. М. Ройтберг, Я. А. |
| author_sort | Los’, V. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:12:04Z |
| description | In a bounded domainG with boundary ∂G that consists of components of different dimensions, we consider an elliptic boundary-value problem in complete scales of Banach spaces. The orders of boundary expressions are arbitrary; they are pseudodifferential along ∂G. We prove the theorem on a complete set of isomorphisms and generalize its application. The results obtained are true for elliptic Sobolev problems with a parameter and parabolic Sobolev problems as well as for systems with the Douglis-Nirenberg structure. |
| first_indexed | 2026-03-24T03:03:59Z |
| format | Article |
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| id | umjimathkievua-article-4714 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:03:59Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/9e/9874c6acbd5621cc3e71300c1afcab9e.pdf |
| spelling | umjimathkievua-article-47142020-03-18T21:12:04Z On the Sobolev problem in the complete scale of Banach spaces О задаче Соболева в полной шкале банаховых пространств Los’, V. M. Roitberg, Ya. A. Лось, В. М. Ройтберг, Я. А. Лось, В. М. Ройтберг, Я. А. In a bounded domainG with boundary ∂G that consists of components of different dimensions, we consider an elliptic boundary-value problem in complete scales of Banach spaces. The orders of boundary expressions are arbitrary; they are pseudodifferential along ∂G. We prove the theorem on a complete set of isomorphisms and generalize its application. The results obtained are true for elliptic Sobolev problems with a parameter and parabolic Sobolev problems as well as for systems with the Douglis-Nirenberg structure. В обмеженій області $G$ з межею $3G$, що складається з компонент різних розмірностей, розглядається еліптична гранична задача в повних шкалах банахових просторів. Порядки граничних виразів довільні, вони псевдодиферепціальиі вздовж $∂G$. Доведено теорему про повний набір ізоморфізмів, розвинуто ЇЇ застосування. Результати залишаються вірними для еліптичних з параметром і параболічних задач Соболева, а також для систем структури Дугліса — Ніренберга. Institute of Mathematics, NAS of Ukraine 1999-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4714 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 9 (1999); 1181–1192 Український математичний журнал; Том 51 № 9 (1999); 1181–1192 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4714/6129 https://umj.imath.kiev.ua/index.php/umj/article/view/4714/6130 Copyright (c) 1999 Los’ V. M.; Roitberg Ya. A. |
| spellingShingle | Los’, V. M. Roitberg, Ya. A. Лось, В. М. Ройтберг, Я. А. Лось, В. М. Ройтберг, Я. А. On the Sobolev problem in the complete scale of Banach spaces |
| title | On the Sobolev problem in the complete scale of Banach spaces |
| title_alt | О задаче Соболева в полной шкале банаховых пространств |
| title_full | On the Sobolev problem in the complete scale of Banach spaces |
| title_fullStr | On the Sobolev problem in the complete scale of Banach spaces |
| title_full_unstemmed | On the Sobolev problem in the complete scale of Banach spaces |
| title_short | On the Sobolev problem in the complete scale of Banach spaces |
| title_sort | on the sobolev problem in the complete scale of banach spaces |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4714 |
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