Partial Differential Equations
Ginzburg–Landau minimizers with prescribed degrees: dependence on domain
[Minimiseurs de l'énergie de Ginzburg–Landau avec degrés prescrits : dépendance du domaine]

Présenté par : Haïm Brezis

Berlyand, Leonid1 ; Mironescu, Petru2
1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
2 Département de mathématiques, Université Paris-Sud, 91405 Orsay cedex, France
Comptes Rendus. Mathématique, Tome 337 (2003) no. 6, pp. 375-380.

On étudie des minimiseurs de l'énergie de Ginzburg–Landau dans un domaine annulaire à trous. Les conditions aux limites sont des degrés prescrits : degrés 1 et −1 sur le bord du domaine annulaire, degré 0 sur les bords des trous. En fonction de la H1-capacité du domaine, les minimiseurs ont deux types de comportement, qualitativement différents. On décrit aussi le comportement des minimiseurs quand le paramètre de Ginzburg–Landau tend vers ∞.

We study minimizers of the Ginzburg–Landau functional in an annular type domain with holes. We assume degrees 1 and −1 on the boundary of the annulus, degree 0 on the boundaries of the holes. Two types of qualitatively different behavior of minimizers occur, depending on the value of the H1-capacity of the domain. We also describe the asymptotic behavior of minimizers as the coherency length tends to ∞.

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DOI : 10.1016/S1631-073X(03)00331-5
Berlyand, Leonid 1 ; Mironescu, Petru 2

1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
2 Département de mathématiques, Université Paris-Sud, 91405 Orsay cedex, France 
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Berlyand, Leonid; Mironescu, Petru. Ginzburg–Landau minimizers with prescribed degrees: dependence on domain. Comptes Rendus. Mathématique, Tome 337 (2003) no. 6, pp. 375-380. doi : 10.1016/S1631-073X(03)00331-5. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00331-5/

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