C1,α convergence of minimizers of a Ginzburg-Landau functional

In this article we study the minimizers of the functional E-s(u, G) = 1/p integral(G)vertical bar del u vertical bar(p) + 1/4 epsilon(p) integral(G) (1 - vertical bar u vertical bar(2))(2), on the class W-g = {v is an element of W-1,W-p(G, R-2); v vertical bar partial derivative G = g}, where g : partial derivative G -> 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-loc(1,alpha)(G, R-2) as epsilon approaches zero.