Pointwise estimates of potentials for higher-order capacities
In a domain D=Ω\E∈ R n , we consider a nonlinear higher-order elliptic equation such that the corresponding energy space is W p m (D)⩜W q 1 (D), q>mp, and estimate a solution u(x) of this equation satisfying the condition u(x)−kf(x)∈W p m (D)⩜W q 1 (D), where k∈R 1, f(x)∈...
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| Date: | 1997 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4993 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511190889791488 |
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| author | Skrypnik, I. V. Скрыпник, И. В. Скрыпник, И. В. |
| author_facet | Skrypnik, I. V. Скрыпник, И. В. Скрыпник, И. В. |
| author_sort | Skrypnik, I. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:22:11Z |
| description | In a domain D=Ω\E∈ R n , we consider a nonlinear higher-order elliptic equation such that the corresponding energy space is W p m (D)⩜W q 1 (D), q>mp, and estimate a solution u(x) of this equation satisfying the condition u(x)−kf(x)∈W p m (D)⩜W q 1 (D), where k∈R 1, f(x)∈ C 0 ∞ (Ω), and f(x)=1 for x∈F. We establish a pointwise estimate for u(x) in terms of the higher-order capacity of the set F and the distance from the point x to the set F. |
| first_indexed | 2026-03-24T03:08:58Z |
| format | Article |
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| id | umjimathkievua-article-4993 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:08:58Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/8b/7c01930d6cf6e76d9b822af51d9b128b.pdf |
| spelling | umjimathkievua-article-49932020-03-18T21:22:11Z Pointwise estimates of potentials for higher-order capacities Поточечные оценки потенциалов для емкости высшего порядка Skrypnik, I. V. Скрыпник, И. В. Скрыпник, И. В. In a domain D=Ω\E∈ R n , we consider a nonlinear higher-order elliptic equation such that the corresponding energy space is W p m (D)⩜W q 1 (D), q>mp, and estimate a solution u(x) of this equation satisfying the condition u(x)−kf(x)∈W p m (D)⩜W q 1 (D), where k∈R 1, f(x)∈ C 0 ∞ (Ω), and f(x)=1 for x∈F. We establish a pointwise estimate for u(x) in terms of the higher-order capacity of the set F and the distance from the point x to the set F. В області D=Ω\E∈ R n розглядається нелінійне еліптичне рівняння вищого порядку при таких припущеннях, що відповідним енергетичним простором є W p m (D)⩜W q 1 (D), q>mp. Оцінюється розв'язок u(x) цього рівняння, який задовольняє умову u(x)−kf(x)∈W p m (D)⩜W q 1 (D), де k∈R 1, f(x)∈ C 0 ∞ (Ω), and f(x)=1 for x∈F.. Доводиться поточкова оцінка u(x) в термінах ємкості вищого порядку множини F і віддалі від точки x до множини F. Institute of Mathematics, NAS of Ukraine 1997-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4993 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 1 (1997); 149–163 Український математичний журнал; Том 49 № 1 (1997); 149–163 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4993/6685 https://umj.imath.kiev.ua/index.php/umj/article/view/4993/6686 Copyright (c) 1997 Skrypnik I. V. |
| spellingShingle | Skrypnik, I. V. Скрыпник, И. В. Скрыпник, И. В. Pointwise estimates of potentials for higher-order capacities |
| title | Pointwise estimates of potentials for higher-order capacities |
| title_alt | Поточечные оценки потенциалов для емкости высшего порядка |
| title_full | Pointwise estimates of potentials for higher-order capacities |
| title_fullStr | Pointwise estimates of potentials for higher-order capacities |
| title_full_unstemmed | Pointwise estimates of potentials for higher-order capacities |
| title_short | Pointwise estimates of potentials for higher-order capacities |
| title_sort | pointwise estimates of potentials for higher-order capacities |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4993 |
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