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1996 Asymptotic behavior for minimizers of a Ginzburg-Landau-type functional in higher dimensions associated with $n$-harmonic maps
Min-Chun Hong
Adv. Differential Equations 1(4): 611-634 (1996).

Abstract

We describe the behavior as $\varepsilon\to 0$ of minimizers for a Ginzburg-Landau functional $$ E_{\varepsilon}(u;\Omega )=\int_{\Omega}\bigl [ \frac {|\nabla u|^n}n +\frac 1{4\varepsilon^n}(1-|u|^2)^2\bigr ]\,dx $$ in the space $H^{1,n}_g(\Omega ;\Bbb R^n)$, where $\Omega\subset\Bbb R^n$ and the boundary data $g:\partial \Omega\to S^{n-1}$ has a nonzero topological degree. Some recent results of Bethuel, Brezis and H\'elein, and of Struwe on the two-dimensional problem, are extended to higher-dimensional cases. New proofs for their results are also presented in this paper.

Citation

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Min-Chun Hong. "Asymptotic behavior for minimizers of a Ginzburg-Landau-type functional in higher dimensions associated with $n$-harmonic maps." Adv. Differential Equations 1 (4) 611 - 634, 1996.

Information

Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0857.35120
MathSciNet: MR1401406

Subjects:
Primary: 58E20
Secondary: 35B40, 35Q55, 49J45

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.1 • No. 4 • 1996
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