Electron. J. Diff. Eqns., Vol. 2000(2000), No. 14, pp. 1-20.

$C^{1,\alpha}$ convergence of minimizers of a Ginzburg-Landau functional

Yutian Lei & Zhuoqun Wu

Abstract:
In this article we study the minimizers of the functional
$ E_\varepsilon(u,G)={1\over p}\int_G|\nabla u|^p +{1 \over 4\varepsilon^p} \int_G(1-|u|^2)^2,$
on the class
$W_g=\{v \in W^{1,p}(G,{\Bbb R}^2);v|_{\partial G}=g\}$,
where $g:\partial G \to S^1$ is a smooth map with Brouwer degree zero, and $p$ is greater than 2. In particular, we show that the minimizer converges to the p-harmonic map in $C_{\hbox{loc}}^{1,\alpha}(G,{\Bbb R}^2)$ as $\varepsilon$ approaches zero.

Submitted September 2, 1999. Published February 21, 2000.
Math Subject Classifications: 35J70.
Key Words: Ginzburg-Landau functional, regularizable minimizer.

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Yutian Lei
Zhuoqun Wu (e-mail: wzq@mail.jlu.edu.cn )
Institute of Mathematics, Jilin University
130023 Changchun, P. R. China
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