Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \geq 7$

Author: 

Ignat, R
Nguyen, L
Slastikov, V
Zarnescu, A

Publication Date: 

14 August 2018

Journal: 

Comptes Rendus Mathématique

Last Updated: 

2020-01-21T13:32:09.55+00:00

Issue: 

9

Volume: 

356

DOI: 

10.1016/j.crma.2018.07.006

page: 

922-926

abstract: 

For ε > 0, we consider the Ginzburg-Landau functional for R N -valued maps defined in the unit ball BN ⊂ R N 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|) x |x| for x ∈ BN .

Symplectic id: 

869329

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article