Geodesic
$C^{1,\alpha}$ convergence of minimizers of a Ginzburg-Landau functional
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35J70
Keywords: Ginzburg-Landau functional, regularizable minimizer 
@article{EJDE_2000__2000__a17,
     author = {Lei, Yutian and Wu, Zhuoqun},
     title = {$C^{1,\alpha}$ convergence of minimizers of a {Ginzburg-Landau} functional},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a17/}
}
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Lei, Yutian; Wu, Zhuoqun. $C^{1,\alpha}$ convergence of minimizers of a Ginzburg-Landau functional. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a17/