On theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains
A notion of $G$-convergence of operators $A_s :\; W_s \rightarrow W_s^*$ to the operator $A:\; W \rightarrow W^*$ is introduced and studied under certain connection conditions for the Banach spaces $W_s,\; s = 1, 2, ... ,$ and the Banach space $W$. It has been established that the connection condi...
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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/5888 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512108876136448 |
|---|---|
| author | Kovalevskii, A. A. Ковалевский, А. А. Ковалевский, А. А. |
| author_facet | Kovalevskii, A. A. Ковалевский, А. А. Ковалевский, А. А. |
| author_sort | Kovalevskii, A. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:20:04Z |
| description | A notion of $G$-convergence of operators $A_s :\; W_s \rightarrow W_s^*$ to the operator $A:\; W \rightarrow W^*$ is introduced and
studied under certain connection conditions for the Banach spaces $W_s,\; s = 1, 2, ... ,$ and the Banach
space $W$. It has been established that the connection conditions for abstract space are satisfied by the
Sobolev spaces $\overset{\circ}{W}^{k, m}(\Omega_s),\quad \overset{\circ}{W}^{k, m}(\Omega)$ ($\{\Omega_s\}$ is a sequence of perforated domains contained in a
bounded domain $\Omega \subset \mathbb{R}^n$). Hence, the results obtained for abstract operators can be applied to the
operators of Dirichlet problems in the domains $\Omega_s$. |
| first_indexed | 2026-03-24T03:23:33Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5888 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:23:33Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ce/da10f88fc1ffa6616572b53d50f993ce.pdf |
| spelling | umjimathkievua-article-58882020-03-19T09:20:04Z On theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains О $G$-сходимости нелинейных эллиптических операторов, связанных с задачей Дирихле в переменных областях Kovalevskii, A. A. Ковалевский, А. А. Ковалевский, А. А. A notion of $G$-convergence of operators $A_s :\; W_s \rightarrow W_s^*$ to the operator $A:\; W \rightarrow W^*$ is introduced and studied under certain connection conditions for the Banach spaces $W_s,\; s = 1, 2, ... ,$ and the Banach space $W$. It has been established that the connection conditions for abstract space are satisfied by the Sobolev spaces $\overset{\circ}{W}^{k, m}(\Omega_s),\quad \overset{\circ}{W}^{k, m}(\Omega)$ ($\{\Omega_s\}$ is a sequence of perforated domains contained in a bounded domain $\Omega \subset \mathbb{R}^n$). Hence, the results obtained for abstract operators can be applied to the operators of Dirichlet problems in the domains $\Omega_s$. При певних умовах зв’язку банахових просторів $W_s,\; s = 1, 2, ... ,$ збанаховим простором $W$ вводиться і вивчається поняття $G$-збіжності операторів $A_s :\; W_s \rightarrow W_s^*$ до оператора $A:\; W \rightarrow W^*$. Встановлюється, що розглядувані умови зв’язку абстрактних просторів задовольняють соболєвські простори $\overset{\circ}{W}^{k, m}(\Omega_s),\quad \overset{\circ}{W}^{k, m}(\Omega)$ ($\{\Omega_s\}$ — послідовність перфорованих областей, що містяться в обмеженій області $\Omega \subset \mathbb{R}^n$), внаслідок чого результати, одержані для абстрактних операторів, можна перенести на оператори задачі Діріхле в областях $\Omega_s$. Institute of Mathematics, NAS of Ukraine 1993-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5888 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 7 (1993); 948–962 Український математичний журнал; Том 45 № 7 (1993); 948–962 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5888/8459 https://umj.imath.kiev.ua/index.php/umj/article/view/5888/8460 Copyright (c) 1993 Kovalevskii A. A. |
| spellingShingle | Kovalevskii, A. A. Ковалевский, А. А. Ковалевский, А. А. On theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains |
| title | On theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains |
| title_alt | О $G$-сходимости нелинейных эллиптических операторов, связанных с задачей Дирихле в переменных областях |
| title_full | On theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains |
| title_fullStr | On theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains |
| title_full_unstemmed | On theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains |
| title_short | On theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains |
| title_sort | on theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5888 |
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