Lorentz space estimates for the Ginzburg-Landau energy

Sylvia Serfaty, Ian Tice

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we prove novel lower bounds for the Ginzburg-Landau energy with or without magnetic field. These bounds rely on an improvement of the "vortex-balls construction" estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz space norm, on which it thus provides an upper bound. The Lorentz space L2, ∞ we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results.

Original languageEnglish (US)
Pages (from-to)773-825
Number of pages53
JournalJournal of Functional Analysis
Volume254
Issue number3
DOIs
StatePublished - Feb 1 2008

Keywords

  • Ball construction
  • Ginzburg-Landau
  • Lorentz spaces Best regards
  • Sylvia Serfaty
  • Vortex balls

ASJC Scopus subject areas

  • Analysis

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