New developments on the Ginzburg-Landau model
type: Item
instance of: scholarly article
title: New developments on the Ginzburg-Landau model
zbMATH Open document ID: 0840.49003
DOI: 10.12775/TMNA.1994.028
published in: Topological Methods in Nonlinear Analysis
publication date: 1996-02-01T00:00:00Z
review text: This expository paper offers a survey of the most important results obtained in the last years in the study of the Ginzburg-Landau equation and gives answers to some open problems raised by \textit{F. Bethuel}, the author and \textit{F. Hélein} in their monograph ``Ginzburg-Landau vortices'' (1994; Zbl 0802.35142). It is emphasized the importance of notions of ``renormalized energy'' and ``canonical harmonic map'' in the study of the asymptotic behavior of minimizers of the Ginzburg-Landau functional. It is also pointed out that the number of vortices heavily depends on the topological Brouwer degree of the initial Dirichlet boundary data. The paper is excellently written and it is a wonderful invitation for the reader to the study of Ginzburg-Landau equations.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 828283
zbMATH Keywords: renormalized energy
zbMATH Keywords: canonical harmonic map
zbMATH Keywords: survey
zbMATH Keywords: Ginzburg-Landau equation
zbMATH Keywords: Brouwer degree
author: Haïm Brezis
MaRDI profile type: Publication
full work available at URL: tmna.1994.028
OpenAlex ID: W2588552699
description: scientific article; zbMATH DE number 828283