Asymptotics for the minimization of a Ginzburg-Landau functional

Fabrice Bethuel, Haim Brezis, Frédéric Hélein

Research output: Contribution to journalArticlepeer-review

260 Scopus citations


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}.

Original languageEnglish (US)
Pages (from-to)123-148
Number of pages26
JournalCalculus of Variations and Partial Differential Equations
Issue number2
StatePublished - May 1993

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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


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