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].
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Received: 10 July 2002 / Accepted: 23 January 2002 / Published online: 5 September 2002
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Sandier, E., Serfaty, S. Ginzburg-Landau minimizers near the first critical field have bounded vorticity. Cal Var 17, 17–28 (2003). https://doi.org/10.1007/s00526-002-0158-9
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DOI: https://doi.org/10.1007/s00526-002-0158-9