Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 14, pp. 1-20.

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

Authors: Yutian Lei (Jilin Univ., P. R. China)
 Zhuoqun Wu (Jilin Univ., P. R. China)
  
Abstract: 
 In this article we study the minimizers of the functional
 $$
 E_\varepsilon(u,G)={1\over p}\int_G|\nabla u|^p+\frac{1 \over 4\varepsilon^p}
 \int_G(1-|u|^2)^2,
 $$
 on the class $W_g=\{v \in W^{1,p}(G,{\mathbb R}^2);v|_{\partial G}=g\}$,
 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 $C_{\hbox{loc}}^{1,\alpha}(G,{\mathbb R}^2)$ as
 $\varepsilon$ approaches zero.

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