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

Y. Lei, Department of Mathematics, Nanjing Normal University, Nanjing, China

E. J. Qualitative Theory of Diff. Equ., No. 22. (2003), pp. 1-21.

Abstract: 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.

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