Nonexistence of Ginzburg-Landau minimizers with prescribed degree on the boundary of a doubly connected domain

Leonid Berlyand, Dmitry Golovaty, Volodymyr Rybalko

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Let ω, Ω be bounded simply connected domains in R2, and let over(ω, ̄) ⊂ Ω. In the annular domain A = Ω {set minus} over(ω, ̄) we consider the class J of complex valued maps having modulus 1 and degree 1 on ∂Ω and ∂ω. We prove that, when cap (A) < π, there exists a finite threshold value κ1 of the Ginzburg-Landau parameter κ such that the minimum of the Ginzburg-Landau energy Eκ not attained in J when κ > κ1 while it is attained when κ < κ1. To cite this article: L. Berlyand et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

Original languageEnglish (US)
Pages (from-to)63-68
Number of pages6
JournalComptes Rendus Mathematique
Volume343
Issue number1
DOIs
StatePublished - Jul 1 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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