Symmetric solutions to minimization of a p-energy functional with ellipsoid value

• Main Author: Yutian Lei
• 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&paramtipus_ertek=publication&param_ertek=174

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.