Lorentz space estimates for the Ginzburg-Landau energy

Sylvia Serfaty, Ian Tice

Research output: Contribution to journalArticle

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

Fingerprint

Lorentz Spaces
Ginzburg-Landau
Vortex
Energy
Estimate
Lower bound
Term
Convergence Results
Ball
Magnetic Field
Upper bound
Norm

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

Lorentz space estimates for the Ginzburg-Landau energy. / Serfaty, Sylvia; Tice, Ian.

In: Journal of Functional Analysis, Vol. 254, No. 3, 01.02.2008, p. 773-825.

Research output: Contribution to journalArticle

Serfaty, Sylvia ; Tice, Ian. / Lorentz space estimates for the Ginzburg-Landau energy. In: Journal of Functional Analysis. 2008 ; Vol. 254, No. 3. pp. 773-825.
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