Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point
We obtain a priori estimates for generalized second derivatives (in the Sobolev weighted norm) of solutions of the Dirichlet problem for the elliptic equation $$\frac{d}{{dx_i }}a_i (x,u,u_x ) + a(x,u,u_x ) = 0,x \in G,$$ in the neighborhood of a conical boundary point of the domain G. We give a...
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| Date: | 1998 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian 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/4816 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510992441540608 |
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| author | Borsuk, M. V. Plesha, M. I. Борсук, М. В. Плеша, М. І. |
| author_facet | Borsuk, M. V. Plesha, M. I. Борсук, М. В. Плеша, М. І. |
| author_sort | Borsuk, M. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:15:12Z |
| description | We obtain a priori estimates for generalized second derivatives (in the Sobolev weighted norm) of solutions of the Dirichlet problem for the elliptic equation $$\frac{d}{{dx_i }}a_i (x,u,u_x ) + a(x,u,u_x ) = 0,x \in G,$$ in the neighborhood of a conical boundary point of the domain G. We give an example that demonstrates that the estimates obtained are almost exact. |
| first_indexed | 2026-03-24T03:05:48Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4816 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:05:48Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ce/e0d675e623adc363256218b20e4c9fce.pdf |
| spelling | umjimathkievua-article-48162020-03-18T21:15:12Z Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point Оцінки узаґальнених розв'язків задачі Діріхле для квазілінійних еліптичних рівнянь другого порядку и області з конічною точкою на межі Borsuk, M. V. Plesha, M. I. Борсук, М. В. Плеша, М. І. We obtain a priori estimates for generalized second derivatives (in the Sobolev weighted norm) of solutions of the Dirichlet problem for the elliptic equation $$\frac{d}{{dx_i }}a_i (x,u,u_x ) + a(x,u,u_x ) = 0,x \in G,$$ in the neighborhood of a conical boundary point of the domain G. We give an example that demonstrates that the estimates obtained are almost exact. Отримані апріорні оцінки других узагальнених похідних (у ваговій соболєвській нормі) розв'язків задачі Діріхле для еліптичного рівняння $$\frac{d}{{dx_i }}a_i (x,u,u_x ) + a(x,u,u_x ) = 0,x \in G,$$ в околі конічної точки межі області $G$. Наведено приклад, який свідчить, що отримані оцінки є майже точними. Institute of Mathematics, NAS of Ukraine 1998-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4816 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 10 (1998); 1299–1309 Український математичний журнал; Том 50 № 10 (1998); 1299–1309 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4816/6331 https://umj.imath.kiev.ua/index.php/umj/article/view/4816/6332 Copyright (c) 1998 Borsuk M. V.; Plesha M. I. |
| spellingShingle | Borsuk, M. V. Plesha, M. I. Борсук, М. В. Плеша, М. І. Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point |
| title | Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point |
| title_alt | Оцінки узаґальнених розв'язків задачі Діріхле для квазілінійних еліптичних рівнянь другого порядку и області з конічною точкою на межі |
| title_full | Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point |
| title_fullStr | Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point |
| title_full_unstemmed | Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point |
| title_short | Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point |
| title_sort | estimates of generalized solutions of the dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4816 |
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