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Pré-Publication, Document De Travail Année : 2011

The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part II: the non-zero degree case

Mickaël dos Santos

Résumé

We consider minimizers of a Ginzburg-Landau energy with a discontinuous and rapidly oscillating pinning term, subject to a Dirichlet boundary condition of degree $d>0$. We prove that minimizers have exactly $d$ isolated zeros (vortices). These vortices are of degree $1$ and pinned by the impurities. As in the standard case studied by Bethuel, Brezis and Hélein, the macroscopic location of vortices is governed by vortex/vortex and vortex/ boundary repelling effects. In some special cases we prove that their macroscopic location tends to minimize the renormalized energy of Bethuel-Brezis-Hélein. In addition, impurities affect the microscopic location of vortices.
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Dates et versions

hal-00587804 , version 1 (21-04-2011)
hal-00587804 , version 2 (22-04-2011)
hal-00587804 , version 3 (29-04-2011)
hal-00587804 , version 4 (06-11-2011)

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Mickaël dos Santos. The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part II: the non-zero degree case. 2011. ⟨hal-00587804v1⟩
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