Ginzburg-Landau minimizers near the first critical field have bounded vorticity |
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| Authors: | E Sandier S Serfaty |
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| Institution: | (1) Université Paris XII Val de Marne, Département de Mathématiques, 61 Avenue du Général de Gaulle, 94010 Créteil, France (e-mail: sandier@univ-paris12.fr) , FR;(2) CMLA, école Normale Supérieure de Cachan, 61 avenue du Président Wilson, 94235 Cachan Cedex, France , FR;(3) Courant Institute of Mathematical Sciences, New York University, 251, Mercer Street, New York, NY 10012, USA (e-mail: serfaty@cims.nyu.edu) , US |
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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 S1, S3] are actually global minimizers. It also
gives a partial answer to a question raised by F. Bethuel and T. Rivière in BR].
Received: 10 July 2002 / Accepted: 23 January 2002 / Published online: 5 September 2002 |
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