Symmetric solutions to minimization of a p-energy functional with ellipsoid value
The author proves the $W^{1,p}$ convergence of the symmetric minimizers $u_{\varepsilon}=(u_{\varepsilon 1},u_{\varepsilon 2},u_{\varepsilon 3})$ of a p-energy functional as $\varepsilon \to 0$, and the zeros of $u_{\varepsilon 1}^2+u_{\varepsilon 2}^2$ are located roughly. In addition,the estimate...
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| Format: | Article |
| Language: | English |
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University of Szeged
2003-12-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=174 |
| _version_ | 1797830791307198464 |
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| author | Yutian Lei |
| author_facet | Yutian Lei |
| author_sort | Yutian Lei |
| collection | DOAJ |
| description | The author proves the $W^{1,p}$ convergence of the symmetric minimizers
$u_{\varepsilon}=(u_{\varepsilon 1},u_{\varepsilon 2},u_{\varepsilon 3})$ of a p-energy functional as $\varepsilon \to 0$, and the zeros of $u_{\varepsilon 1}^2+u_{\varepsilon 2}^2$ are located roughly. In addition,the estimates of the convergent rate of $u_{\varepsilon 3}^2$ (to $0$) are presented. At last, based on researching the Euler-Lagrange equation of symmetric solutions and establishing its $C^{1,\alpha}$ estimate, the author obtains the $C^{1,\alpha}$ convergence of some symmetric minimizer. |
| first_indexed | 2024-04-09T13:41:46Z |
| format | Article |
| id | doaj.art-8e625afbb93c4adcb6f850cc6b6179ad |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:46Z |
| publishDate | 2003-12-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-8e625afbb93c4adcb6f850cc6b6179ad2023-05-09T07:52:57ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752003-12-0120032212110.14232/ejqtde.2003.1.22174Symmetric solutions to minimization of a p-energy functional with ellipsoid valueYutian Lei0Department of Mathematics, Nanjing Normal University, Nanjing, ChinaThe author proves the $W^{1,p}$ convergence of the symmetric minimizers $u_{\varepsilon}=(u_{\varepsilon 1},u_{\varepsilon 2},u_{\varepsilon 3})$ of a p-energy functional as $\varepsilon \to 0$, and the zeros of $u_{\varepsilon 1}^2+u_{\varepsilon 2}^2$ are located roughly. In addition,the estimates of the convergent rate of $u_{\varepsilon 3}^2$ (to $0$) are presented. At last, based on researching the Euler-Lagrange equation of symmetric solutions and establishing its $C^{1,\alpha}$ estimate, the author obtains the $C^{1,\alpha}$ convergence of some symmetric minimizer.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=174 |
| spellingShingle | Yutian Lei Symmetric solutions to minimization of a p-energy functional with ellipsoid value Electronic Journal of Qualitative Theory of Differential Equations |
| title | Symmetric solutions to minimization of a p-energy functional with ellipsoid value |
| title_full | Symmetric solutions to minimization of a p-energy functional with ellipsoid value |
| title_fullStr | Symmetric solutions to minimization of a p-energy functional with ellipsoid value |
| title_full_unstemmed | Symmetric solutions to minimization of a p-energy functional with ellipsoid value |
| title_short | Symmetric solutions to minimization of a p-energy functional with ellipsoid value |
| title_sort | symmetric solutions to minimization of a p energy functional with ellipsoid value |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=174 |
| work_keys_str_mv | AT yutianlei symmetricsolutionstominimizationofapenergyfunctionalwithellipsoidvalue |