Ginzburg–Landau minimizers with prescribed degrees: dependence on domain

Leonid Berlyand; Petru Mironescu

doi:10.1016/S1631-073X(03)00331-5

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

Leonid Berlyand ¹ ; Petru Mironescu 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

Comptes Rendus. Mathématique, Volume 337 (2003) no. 6, pp. 375-380.

Résumé
Abstract

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 ∞.

Reçu le : 2003-06-20
Accepté le : 2003-06-20
Publié le : 2003-09-03

DOI : 10.1016/S1631-073X(03)00331-5

Affiliations des auteurs :

Leonid Berlyand ¹ ; Petru Mironescu 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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     author = {Leonid Berlyand and Petru Mironescu},
     title = {Ginzburg{\textendash}Landau minimizers with prescribed degrees: dependence on domain},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {375--380},
     publisher = {Elsevier},
     volume = {337},
     number = {6},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00331-5},
     language = {en},
}

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Leonid Berlyand; Petru Mironescu. Ginzburg–Landau minimizers with prescribed degrees: dependence on domain. Comptes Rendus. Mathématique, Volume 337 (2003) no. 6, pp. 375-380. doi : 10.1016/S1631-073X(03)00331-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00331-5/

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