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

Issue		ESAIM: COCV Volume 16, Number 3, July-September 2010


Page(s)		545 - 580
DOI		10.1051/cocv/2009009
Published online		18 June 2009

ESAIM: COCV 16 (2010) 545-580

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

Ayman Kachmar¹^,2

¹ 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: 30 April 2008
Revised: 13 February 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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