Hölder continuity and the Harnack inequality for the solutions of an elliptic equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain
We consider quasilinear equations of the $p$-Laplacian type uniformly degenerating in a part of the domain. An analog of the Harnack inequality is proved for nonnegative solutions and the Holder continuity of the solutions is established by using this inequality.
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| Date: | 2017 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2017
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1806 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865788797636050944 |
|---|---|
| author | Huseynov, S. T. Гусейнов, С. Т. |
| author_facet | Huseynov, S. T. Гусейнов, С. Т. |
| author_institution_txt_mv | [
{
"author": "С. Т. Гусейнов",
"institution": null
}
] |
| author_sort | Huseynov, S. T. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2019-12-05T09:28:05Z |
| description | We consider quasilinear equations of the $p$-Laplacian type uniformly degenerating in a part of the domain. An analog of the
Harnack inequality is proved for nonnegative solutions and the Holder continuity of the solutions is established by using
this inequality. |
| first_indexed | 2026-03-24T02:12:59Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-1806 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T02:12:59Z |
| publishDate | 2017 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-18062019-12-05T09:28:05Z Hölder continuity and the Harnack inequality for the solutions of an elliptic equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain Гельдерова непрерывность и неравенство Харнака для решений равномерно вырождающегося в части области эллиптического уравнения, содержащего $p$-лапласиан Huseynov, S. T. Гусейнов, С. Т. We consider quasilinear equations of the $p$-Laplacian type uniformly degenerating in a part of the domain. An analog of the Harnack inequality is proved for nonnegative solutions and the Holder continuity of the solutions is established by using this inequality. Розглядаються квазiлiнiйнi рiвняння типу $p$-лапласiана, що рiвномiрно вироджуються в частинi областi. Доведено аналог нерiвностi Харнака для невiд’ємних розв’язкiв, за допомогою якого встановлено гельдерову неперервнiсть розв’язкiв. Institute of Mathematics, NAS of Ukraine 2017-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/1806 Ukrains’kyi Matematychnyi Zhurnal; Vol. 69 No. 12 (2017); 1596-1604 Український математичний журнал; Том 69 № 12 (2017); 1596-1604 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/1806/788 Copyright (c) 2017 Huseynov S. T. |
| spellingShingle | Huseynov, S. T. Гусейнов, С. Т. Hölder continuity and the Harnack inequality for the solutions of an elliptic equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain |
| title | Hölder continuity and the Harnack inequality for the solutions of an elliptic
equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain |
| title_alt | Гельдерова непрерывность и неравенство Харнака для решений равномерно вырождающегося в части области эллиптического уравнения, содержащего $p$-лапласиан |
| title_full | Hölder continuity and the Harnack inequality for the solutions of an elliptic
equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain |
| title_fullStr | Hölder continuity and the Harnack inequality for the solutions of an elliptic
equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain |
| title_full_unstemmed | Hölder continuity and the Harnack inequality for the solutions of an elliptic
equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain |
| title_short | Hölder continuity and the Harnack inequality for the solutions of an elliptic
equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain |
| title_sort | hölder continuity and the harnack inequality for the solutions of an elliptic
equation containing the $p$ -laplacian and uniformly degenerating in a part of the domain |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/1806 |
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