**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.

Communicated by G. Makay.
| Appeared on 2003-12-23 |

**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.

You can download the full text of this paper in DVI, PostScript or PDF format.