Unicité du tourbillon de Ginzburg–Landau de degré un dans la boule unité en dimension N ≥ 7

Radu Ignat; Luc Nguyen; Valeriy Slastikov; Arghir Zarnescu

doi:10.1016/j.crma.2018.07.006

Unicité du tourbillon de Ginzburg–Landau de degré un dans la boule unité en dimension N ≥ 7

Translated title of the contribution: Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7

Radu Ignat, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

For ε>0, we consider the Ginzburg–Landau functional for R^N-valued maps defined in the unit ball B^N⊂R^N with the vortex boundary data x on ∂B^N. In dimensions N≥7, we prove that, for every ε>0, there exists a unique global minimizer u_ε of this problem; moreover, u_ε is symmetric and of the form u_ε(x)=f_ε(|x|)[Formula presented] for x∈B^N.

Translated title of the contribution	Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7
Original language	French
Pages (from-to)	922-926
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	356
Issue number	9
Early online date	14 Aug 2018
DOIs	https://doi.org/10.1016/j.crma.2018.07.006
Publication status	Published - 1 Sept 2018

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https://arxiv.org/abs/1806.10453

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title = "Unicit{\'e} du tourbillon de Ginzburg–Landau de degr{\'e} un dans la boule unit{\'e} en dimension N ≥ 7",

abstract = "For ε>0, we consider the Ginzburg–Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, 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|)[Formula presented] for x∈BN.",

author = "Radu Ignat and Luc Nguyen and Valeriy Slastikov and Arghir Zarnescu",

year = "2018",

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T1 - Unicité du tourbillon de Ginzburg–Landau de degré un dans la boule unité en dimension N ≥ 7

AU - Ignat, Radu

AU - Nguyen, Luc

AU - Slastikov, Valeriy

AU - Zarnescu, Arghir

PY - 2018/9/1

Y1 - 2018/9/1

N2 - For ε>0, we consider the Ginzburg–Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, 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|)[Formula presented] for x∈BN.

AB - For ε>0, we consider the Ginzburg–Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, 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|)[Formula presented] for x∈BN.

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UR - https://arxiv.org/abs/1806.10453

U2 - 10.1016/j.crma.2018.07.006

DO - 10.1016/j.crma.2018.07.006

M3 - Article (Academic Journal)

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SN - 1631-073X

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 9

ER -

Unicité du tourbillon de Ginzburg–Landau de degré un dans la boule unité en dimension N ≥ 7

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Unicité du tourbillon de Ginzburg–Landau de degré un dans la boule unité en dimension N ≥ 7

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Unicité du tourbillon de Ginzburg–Landau de degré un dans la boule unité en dimension N ≥ 7