Differential and Integral Equations

Asymptotic behavior for minimizers of an anisotropic Ginzburg-Landau functional

Shijin Ding and Zuhan Liu

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Minimizers $u_{\varepsilon}$ of some anisotropic Ginzburg-Landau functional $E_{\varepsilon}$ defined in (1.4) below on a smooth domain ${\Omega}\subset R^2$ with smooth boundary data of degree $d$ are shown to subconverge (as ${\varepsilon}\to 0$) locally in $C^{1+{\alpha}}$ away from finitely many points $a_1,\ldots,a_N$ to an anisotropic harmonic map $u_*$: ${\Omega}\setminus \{a_1,\ldots,a_N\}$ $\to$ $R^2$ where $\{a_1,\ldots,a_N\}\subset{\Omega} \cap a^{-1}(m)$, $N$ is related to the degree $d$, $m,a^{-1}(m)$ are defined in the following.

Article information

Differential Integral Equations, Volume 13, Number 1-3 (2000), 227-254.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B25: Singular perturbations
Secondary: 35J20: Variational methods for second-order elliptic equations 35Q40: PDEs in connection with quantum mechanics


Ding, Shijin; Liu, Zuhan. Asymptotic behavior for minimizers of an anisotropic Ginzburg-Landau functional. Differential Integral Equations 13 (2000), no. 1-3, 227--254. https://projecteuclid.org/euclid.die/1356124298

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