Asymptotics for the minimization of a Ginzburg-Landau functional

Fabrice Bethuel; Haim Brezis; Frédéric Hélein

doi:10.1007/BF01191614

Asymptotics for the minimization of a Ginzburg-Landau functional

Fabrice Bethuel, Haim Brezis, Frédéric Hélein

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

260 Scopus citations

Abstract

Let Ω ⊂ ℝ² be a smooth bounded simply connected domain. Consider the functional {Mathematical expression} on the class H_g¹={u εH¹(Ω; ℂ);u=g on ∂Ω} where g:∂Ω∂ → ℂ is a prescribed smooth map with |g|=1 on ∂Ω∂ and deg(g, ∂Ω)=0. Let u u_ε be a minimizer for E_ε on H_g¹. We prove that u_ε → u₀ in {Mathematical expression} as ε → 0, where u₀ is identified. Moreover {Mathematical expression}.

Original language	English (US)
Pages (from-to)	123-148
Number of pages	26
Journal	Calculus of Variations and Partial Differential Equations
Volume	1
Issue number	2
DOIs	https://doi.org/10.1007/BF01191614
State	Published - May 1993

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

Mathematics subject classification: 35B25, 35B40, 35J55, 35J60

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10.1007/BF01191614

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abstract = "Let Ω ⊂ ℝ2 be a smooth bounded simply connected domain. Consider the functional {Mathematical expression} on the class Hg1={u εH1(Ω; ℂ);u=g on ∂Ω} where g:∂Ω∂ → ℂ is a prescribed smooth map with |g|=1 on ∂Ω∂ and deg(g, ∂Ω)=0. Let u uε be a minimizer for Eε on Hg1. We prove that uε → u0 in {Mathematical expression} as ε → 0, where u0 is identified. Moreover {Mathematical expression}.",

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T1 - Asymptotics for the minimization of a Ginzburg-Landau functional

AU - Bethuel, Fabrice

AU - Brezis, Haim

AU - Hélein, Frédéric

PY - 1993/5

Y1 - 1993/5

N2 - Let Ω ⊂ ℝ2 be a smooth bounded simply connected domain. Consider the functional {Mathematical expression} on the class Hg1={u εH1(Ω; ℂ);u=g on ∂Ω} where g:∂Ω∂ → ℂ is a prescribed smooth map with |g|=1 on ∂Ω∂ and deg(g, ∂Ω)=0. Let u uε be a minimizer for Eε on Hg1. We prove that uε → u0 in {Mathematical expression} as ε → 0, where u0 is identified. Moreover {Mathematical expression}.

AB - Let Ω ⊂ ℝ2 be a smooth bounded simply connected domain. Consider the functional {Mathematical expression} on the class Hg1={u εH1(Ω; ℂ);u=g on ∂Ω} where g:∂Ω∂ → ℂ is a prescribed smooth map with |g|=1 on ∂Ω∂ and deg(g, ∂Ω)=0. Let u uε be a minimizer for Eε on Hg1. We prove that uε → u0 in {Mathematical expression} as ε → 0, where u0 is identified. Moreover {Mathematical expression}.

KW - Mathematics subject classification: 35B25, 35B40, 35J55, 35J60

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Asymptotics for the minimization of a Ginzburg-Landau functional

Abstract

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