Principle of additivity in averaging of degenerate nonlinear Dirichlet problems
We study the problem of averaging of Dirichlet problems for degenerate nonlinear elliptic equations of the second order in domains with fine-grained boundary under the condition that the weight function belongs to a certain Muckenhoupt class. We prove a pointwise estimate for solutions of the model...
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| Date: | 1998 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4977 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511169661370368 |
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| author | Larin, D. V. Skrypnik, I. V. Ларин, Д. В. Скрыпник, И. В. Ларин, Д. В. Скрыпник, И. В. |
| author_facet | Larin, D. V. Skrypnik, I. V. Ларин, Д. В. Скрыпник, И. В. Ларин, Д. В. Скрыпник, И. В. |
| author_sort | Larin, D. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:21:24Z |
| description | We study the problem of averaging of Dirichlet problems for degenerate nonlinear elliptic equations of the second order in domains with fine-grained boundary under the condition that the weight function belongs to a certain Muckenhoupt class. We prove a pointwise estimate for solutions of the model degenerate nonlinear problem. The averaged boundary-value problem is constructed under new structural conditions for a perforated domain. In particular, we do not assume that the diameters of cavities are small as compared with the distances between them. |
| first_indexed | 2026-03-24T03:08:37Z |
| format | Article |
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| id | umjimathkievua-article-4977 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:08:37Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/16/1aa7e44dc76a01b808b695b70415a416.pdf |
| spelling | umjimathkievua-article-49772020-03-18T21:21:24Z Principle of additivity in averaging of degenerate nonlinear Dirichlet problems Принцип аддитивности в усреднении вырождающихся нелинейных задач Дирихле Larin, D. V. Skrypnik, I. V. Ларин, Д. В. Скрыпник, И. В. Ларин, Д. В. Скрыпник, И. В. We study the problem of averaging of Dirichlet problems for degenerate nonlinear elliptic equations of the second order in domains with fine-grained boundary under the condition that the weight function belongs to a certain Muckenhoupt class. We prove a pointwise estimate for solutions of the model degenerate nonlinear problem. The averaged boundary-value problem is constructed under new structural conditions for a perforated domain. In particular, we do not assume that the diameters of cavities are small as compared with the distances between them. Вивчається усереднення задач Діріхле для вироджених нелінійних еліптичних рівнянь другого порядку в областях з дрібнозернистою межею за умови, що вагова функція належить до певного класу Макенхаупта. Доведено поточкову оцінку розв'язків модельної виродженої нелінійної задачі. Побудовано усереднену граничну задачу при нових структурних умовах відносно перфорованої області. Зокрема, не припускається малість діаметрів порожнин відносно віддалей між ними. Institute of Mathematics, NAS of Ukraine 1998-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4977 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 1 (1998); 118–135 Український математичний журнал; Том 50 № 1 (1998); 118–135 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4977/6653 https://umj.imath.kiev.ua/index.php/umj/article/view/4977/6654 Copyright (c) 1998 Larin D. V.; Skrypnik I. V. |
| spellingShingle | Larin, D. V. Skrypnik, I. V. Ларин, Д. В. Скрыпник, И. В. Ларин, Д. В. Скрыпник, И. В. Principle of additivity in averaging of degenerate nonlinear Dirichlet problems |
| title | Principle of additivity in averaging of degenerate nonlinear Dirichlet problems |
| title_alt | Принцип аддитивности в усреднении вырождающихся
нелинейных задач Дирихле |
| title_full | Principle of additivity in averaging of degenerate nonlinear Dirichlet problems |
| title_fullStr | Principle of additivity in averaging of degenerate nonlinear Dirichlet problems |
| title_full_unstemmed | Principle of additivity in averaging of degenerate nonlinear Dirichlet problems |
| title_short | Principle of additivity in averaging of degenerate nonlinear Dirichlet problems |
| title_sort | principle of additivity in averaging of degenerate nonlinear dirichlet problems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4977 |
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