Ginzburg-Landau minimizers near the first critical field have bounded vorticity

Etienne Sandier; Sylvia Serfaty

doi:10.1007/s00526-002-0158-9

Ginzburg-Landau minimizers near the first critical field have bounded vorticity

Etienne Sandier, Sylvia Serfaty

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that for fields close enough to the first critical field, minimizers of the Ginzburg-Landau functional have a number of vortices bounded independently from the Ginzburg-Landau parameter. This generalizes a result proved in [SS1] and shows that locally minimizing solutions of the Ginzburg-Landau equation found in [Sl, S3] are actually global minimizers. It also gives a partial answer to a question raised by F. Bethuel and T. Rivière in [BR].

Original language	English (US)
Pages (from-to)	17-28
Number of pages	12
Journal	Calculus of Variations and Partial Differential Equations
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/s00526-002-0158-9
State	Published - May 2003

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "We prove that for fields close enough to the first critical field, minimizers of the Ginzburg-Landau functional have a number of vortices bounded independently from the Ginzburg-Landau parameter. This generalizes a result proved in [SS1] and shows that locally minimizing solutions of the Ginzburg-Landau equation found in [Sl, S3] are actually global minimizers. It also gives a partial answer to a question raised by F. Bethuel and T. Rivi{\`e}re in [BR].",

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Ginzburg-Landau minimizers near the first critical field have bounded vorticity

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