Relaxation in magnetostriction
type: Item
instance of: scholarly article
title: Relaxation in magnetostriction
zbMATH Open document ID: 0951.49020
DOI: 10.1007/PL00013456
author: Pablo Pedregal
published in: Calculus of Variations and Partial Differential Equations
publication date: 2000-12-18T00:00:00Z
review text: The author carries out the relaxation process for the class of nonlocal functionals defined as \[ I(m)=\int_\Omega \phi(x,u(x),m(x)) dx+ \int_\Omega\psi(x,u(x),\nabla u(x)) dx, \] where \(\Omega\) is an open subset of \({\mathbb R}^N\), \(m\in L^2(\Omega)\) and \(u\in H^1_0(\Omega)\) are coupled by the nonlocal differential constraint \[ \text{div}(-\nabla u+m)=0. \] The relaxed functional is computed in terms of Young measures associated with minimizing sequences of \(I\). In dimension two the magnetostriction functional is discussed in detail, and under some simplifying assumptions.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 74F15
zbMATH DE Number: 1406313
zbMATH Keywords: relaxation
zbMATH Keywords: Young measures
zbMATH Keywords: nonlocal problems
MaRDI profile type: Publication
full work available at URL: pl00013456
OpenAlex ID: W2013244021
description: scientific article; zbMATH DE number 1406313