PreprintCC BY 4.0arXiv
Global minimality of the degree-one Ginzburg-Landau vortex solution in the unit ball in dimensions n ≥ 2
Abstract
We consider the problem of minimizing the Ginzburg-Landau functional among ℝn-valued maps from the unit ball B ⊂ ℝn with vortex boundary condition u(x) = x on ∂ B. We show that, for every Ginzburg-Landau parameter ε > 0, there exists a unique minimizer given exactly by the rotationally symmetric vortex solution in dimension n≥ 2.
Related
- A Solution of Problem 2.5 by Brezis on the Planar Ginzburg--Landau Equation
- Using the Renormalized Energy from Ginzburg-Landau Theory to Compute Solution Landscapes in the Reduced Landau-de Gennes Theory
- A remark on the global minimality of the cracktip
- Global minimality of lamellae for isotropic Ohta--Kawasaki and Yukawa energies
- Global Minimality of Matrix-Valued Heteroclinic Connections between Vacuum Orbits
BibTeX
@misc{ignat2026global,
title = {{Global minimality of the degree-one Ginzburg-Landau vortex solution in the unit ball in dimensions $n \geq 2$}},
author = {Radu Ignat and Luc Nguyen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35398},
eprint = {2609.35398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35398},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global minimality of the degree-one Ginzburg-Landau vortex solution in the unit ball in dimensions n ≥ 2
AU - Radu Ignat
AU - Luc Nguyen
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35398
UR - https://arxiv.org/abs/2609.35398
AB - We consider the problem of minimizing the Ginzburg-Landau functional among ℝ^n-valued maps from the unit ball B ⊂ ℝ^n with vortex boundary condition u(x) = x on ∂ B. We show that, for every Ginzburg-Landau parameter ε > 0, there exists a unique minimizer given exactly by the rotationally symmetric vortex solution in dimension n≥ 2.
ER -