Work

Global minimality of the degree-one Ginzburg-Landau vortex solution in the unit ball in dimensions $n \geq 2$

Year: 2026

Type: preprint

Abstract: We consider the problem of minimizing the Ginzburg-Landau functional among $\mathbb{R}^n$-valued maps from the unit ball $B \subset \mathbb{R}^n$ with vortex boundary condition $u(x) = x$ on $\partial B$. We show that, for every Ginzburg-Landau parameter $\varepsilon > 0$, there exists a unique minimizer given exactly by the rotationally symmetric vortex solution in dimension $n\geq 2$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.35398

Authors: Ignat, Radu, Nguyen, Luc

Institutions: Centre National de la Recherche Scientifique, Université Toulouse III - Paul Sabatier, Université de Toulouse, Institut de Mathématiques de Toulouse, University of Oxford

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: Singularities of energy-minimizing vector-valued maps, Modeling and Simulation of Complex Ferromagnetic Systems

OpenAlex ID: W7214771569

Cites: 1

Cited by: 2

Related to: 10