On the Ginzburg-Landau energy with a weight vanishing at the boundary
type: Item
instance of: scholarly article
title: On the Ginzburg-Landau energy with a weight vanishing at the boundary
zbMATH Open document ID: 0964.35144
DOI: 10.1016/S0362-546X(99)00196-0
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-07-02T00:00:00Z
review text: The paper studies the behavior as \(\varepsilon \to 0\) of the minimizers of the Ginzburg--Landau energy with weight \[ E^w_\varepsilon (u)= {1\over 2} \int_G |\nabla u|^2+ {1\over {4\varepsilon^2}} \int_G (1-|u|^2)^2w \] in the class \(H^1_g(G)=\{u\in H^1(G;{\mathbb R}^2): u=g\) on \(\partial G\},\) where \(G\subset {\mathbb R}^2\) is a smooth and bounded domain and \(g:\partial G\to S^1\) is a smooth function with topological degree \(d>0.\) The weight \(w\) is of the type \[ w(z)=|z-z_0|^p+f(z), \] with \(f\in C^1(\overline{G}),\) \(f(z)=o(|z-z_0|^p),\) \(|\nabla f(z)|=o(|z-z_0|^{p-1})\) in a neighborhood of \(z_0\in \partial G\) and \(p>1.\)
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 1556811
zbMATH Keywords: Ginzburg-Landau energy
zbMATH Keywords: renormalized energy
zbMATH Keywords: harmonic map
zbMATH Keywords: vanishing weight
author: Cătălin-George Lefter
MaRDI profile type: Publication
cites work: Asymptotics for the minimization of a Ginzburg-Landau functional
cites work: Q3142972
cites work: Q4012529
cites work: Q4856126
cites work: On the Ginzburg-Landau energy with weight
cites work: Q4862650
cites work: Q4344325
cites work: Q4272495
cites work: On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions
full work available at URL: s0362-546x(99)00196-0
OpenAlex ID: W2074314597
description: scientific article; zbMATH DE number 1556811