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

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

14 August 2018

## Journal:

Comptes Rendus Mathématique

## Last Updated:

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

9

356

## DOI:

10.1016/j.crma.2018.07.006

922-926

## abstract:

For ε &gt; 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 &gt; 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 .

869329

Not Submitted

Journal Article