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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2003-12-01
|
| 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 |
| Summary: | 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. |
|---|---|
| ISSN: | 1417-3875 1417-3875 |