A relaxation result for micromagnetics in SBV
type: Item
instance of: scholarly article
title: A relaxation result for micromagnetics in SBV
zbMATH Open document ID: 1179.35018
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2009-09-02T00:00:00Z
review text: The paper deals with minimization problems for functionals of the form \[ E(m) = \int_{\Omega} f (x, m(x), \triangledown m(x)) \,dx+ \int_{\Omega \cap S(m)} \big|[m](x)\big| \,dH^{N -1} +E_1 (m), \] where \(E_1\) is a continuous functional in the \(L^2\) norm, \([m]\) is the jump of \(m, S(m)\) is the set of discontinuities of \(m\), and \(m\) satisfies the pointwise constraint \(|m(x)| = 1\). Problems of this kind arise in some continuum models in micromagnetics. The correct framework to set the problem is the one of SBV spaces, and an important issue consists in characterizing the lower semicontinuous envelope of \(E\): \[ \inf \Big\{\lim_n \inf E(m_n ): |m_n|=1,\;m_n\rightarrow m\text{ in }L^1\Big\} . \] In the paper this characterization is provided under mild and natural assumptions on the integrand \(f\).
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35D99
Mathematics Subject Classification ID: 35E99
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 5601459
zbMATH Keywords: integral representation
zbMATH Keywords: quasiconvexification
zbMATH Keywords: lower semicontinuous envelope
author: Pedro Miguel Santos
reviewed by: Giuseppe Buttazzo
MaRDI profile type: Publication
full work available at URL: s00030-009-0016-y
OpenAlex ID: W2092727548
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DOI: 10.1007/S00030-009-0016-Y
description: scientific article; zbMATH DE number 5601459