Partial differential equations/Calculus of variations
Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7
Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 922-926.

For ε>0, we consider the Ginzburg–Landau functional for RN-valued maps defined in the unit ball BNRN with the vortex boundary data x on BN. In dimensions N7, we prove that, for every ε>0, there exists a unique global minimizer uε of this problem; moreover, uε is symmetric and of the form uε(x)=fε(|x|)x|x| for xBN.

Nous considérons la fonctionnelle de Ginzburg–Landau pour les applications à valeurs dans RN définies dans la boule unité BNRN avec la donnée de tourbillon x au bord BN. En dimension N7, nous montrons que, pour tout ε>0, il existe un unique minimiseur global uε à ce problème ; de plus, uε est symétrique de la forme uε(x)=fε(|x|)x|x| pour xBN.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.07.006
Ignat, Radu 1; Nguyen, Luc 2; Slastikov, Valeriy 3; Zarnescu, Arghir 4, 5, 6

1 Institut de mathématiques de Toulouse & Institut universitaire de France, UMR 5219, Université de Toulouse, CNRS, UPS IMT, 31062 Toulouse cedex 9, France
2 Mathematical Institute and St Edmund Hall, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom
3 School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom
4 IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013, Bilbao, Bizkaia, Spain
5 BCAM, Basque Center for Applied Mathematics, Mazarredo 14, E48009 Bilbao, Bizkaia, Spain
6 “Simion Stoilow” Institute of the Romanian Academy, 21 Calea Griviţei, 010702 Bucharest, Romania
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Ignat, Radu; Nguyen, Luc; Slastikov, Valeriy; Zarnescu, Arghir. Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7. Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 922-926. doi : 10.1016/j.crma.2018.07.006. http://www.numdam.org/articles/10.1016/j.crma.2018.07.006/

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