Publication ahead of print Issue ESAIM: COCV DOI 10.1051/cocv/2009009 Published online 18 June 2009

ESAIM: COCV
DOI: 10.1051/cocv/2009009

Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint

Ayman Kachmar<sup>1, 2

1</sup>  Université Paris-Sud, Département de mathématique, Bât. 425, 91405 Orsay, France.
²  Aarhus University, Department of mathematical sciences, 1530 Ny Munkegade, 8000 Aarhus C, Denmark. ayman.kachmar@math.u-psud.fr

Received April 30, 2008. Revised February 13, 2009. Published online June 18, 2009.

Abstract
This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied magnetic field for vortex nucleation is estimated in the London singular limit, and as a by-product, results concerning vortex-pinning and boundary conditions on the interface are obtained.

Mathematics Subject Classification. 35J60, 35J20, 35J25, 35B40, 35Q55, 82D55

Key words: Generalized Ginzburg-Landau energy functional, proximity effects, global minimizers, unique positive solution, vortices


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