C1-alpha convergence of minimizers of a Ginzburg-Landau functional
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 g...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2000-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2000/14/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |