Limiting behavior of the Ginzburg-Landau functional

Robert L. Jerrard, Halil Mete Soner

Research output: Contribution to journalArticle

29 Scopus citations

Abstract

We continue our study of the functional for u ε H1 (U; ℝ2), where U is a bounded, open subset of ℝ2. Compactness results for the scaled Jacobian of ue are proved under the assumption that Ee(ue) is bounded uniformly by a function of e. In addition, the Gamma limit of Ee(ue)/(ln e)2 is shown to be where v is the limit of j(ue)/ ln e , j(ue) := ue x Due, and ∥ · ∥ is the total variation of a Radon measure. These results are applied to the Ginzburg-Landau functional with external magnetic field hext ≈ H ln e . The Gamma limit of Fe/(ln e)2 is calculated to be where v is as before, and a is the limit of Ae/ ln e .

Original languageEnglish (US)
Pages (from-to)524-561
Number of pages38
JournalJournal of Functional Analysis
Volume192
Issue number2
DOIs
StatePublished - Jul 10 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • BnV
  • Compactness
  • Gamma limit
  • Ginzburg-Landau functional

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