C1-alpha convergence of minimizers of a Ginzburg-Landau functional

• Main Authors: Yutian Lei, Zhuoqun Wu
• Format: Article
• Language: English
• Published: Texas State University 2000-02-01
• Series: Electronic Journal of Differential Equations
• Subjects: Ginzburg-Landau functional; regularizable minimizer.
• Online Access: http://ejde.math.txstate.edu/Volumes/2000/14/abstr.html

In this article we study the minimizers of the functional $$ E_varepsilon(u,G)={1over p}int_G|abla u|^p+frac{1 over 4varepsilon^p} int_G(1-|u|^2)^2, $$ on the class $W_g={v in W^{1,p}(G,{mathbb R}^2);v|_{partial G}=g}$, where $g:partial G o S^1$ 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.