Geodesic
\(C^{1,\alpha}\) convergence of minimizers of a Ginzburg-Landau functional
Electronic journal of differential equations, Tome 2000 (2000)
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__a90,
     author = {Lei,  Yutian and Wu,  Zhuoqun},
     title = {\(C^{1,\alpha}\) convergence of minimizers of a {Ginzburg-Landau} functional},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0939.35076},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a90/}
}
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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__a90/