Regularity for micromagnetic configurations having zero jump energy
type: Item
instance of: scholarly article
title: Regularity for micromagnetic configurations having zero jump energy
zbMATH Open document ID: 1021.35023
author: Myriam Lecumberry
author: Tristan Rivière
published in: Calculus of Variations and Partial Differential Equations
publication date: 2003-03-17T00:00:00Z
review text: The authors consider the following family of energy-functionals, related to micromagnetics, that is \[ E_\varepsilon(u)=\int_\Omega \frac{\varepsilon}{2}|\nabla u|^2+\frac 1{2\varepsilon} \int_{\mathbb{R}^2}H^2_u dx, \] where \(\Omega\) is a bounded domain of \(\mathbb{R}^2\), \(u\in H^1(\Omega,S^1)\) is the vector field corresponding to magnetization and \(H_u\) is the demagnetizing vector field, defined by \[ \begin{cases} \text{div}(\overline{u}+Hu)=0 & \text{in }\mathbb{R}^2,\\ \text{curl} H_u=0 & \text{in }\mathbb{R}^2,\end{cases} \] where \(\overline u\) is the extension of \(u\) by 0 out of \(\Omega\). The authors study asymptotic behaviour of \(E_\varepsilon\).
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1883395
zbMATH Keywords: magnetization
zbMATH Keywords: demagnetizing vector field
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s005260100132
OpenAlex ID: W2059420064
DOI: 10.1007/S005260100132
description: scientific article; zbMATH DE number 1883395