\(A\)-\(B\) quasiconvexity and implicit partial differential equations
type: Item
instance of: scholarly article
title: \(A\)-\(B\) quasiconvexity and implicit partial differential equations
zbMATH Open document ID: 1030.35022
author: Bernard Dacorogna
author: Irene Fonseca
published in: Calculus of Variations and Partial Differential Equations
publication date: 2002-06-17T00:00:00Z
review text: This paper deals with the following boundary value problem in \(\Omega\) open subset of \(\mathbb{R} ^n\) for differential inclusion: \[ Bu(x)\in E \] with \(u=\varphi\) on \(\partial \Omega \) where \(\varphi \in C^{1} _{\text{pie}}(\overline \Omega , \mathbb{R}^N)\), \(E\) is a compact subset of \(\mathbb{R}^{mn}\) and B is a \(m n\) -valued first order differential operator. In the framework of \(A\)-\(B\)-quasiconvexity, the authors prove the existence of solution \(u\in C^{1} _{\text{pie}}(\overline \Omega , \mathbb{R}^N)\) with \(Bu \in L^\infty\) when \(\varphi\) satisfies the compatibility condition. Moreover the authors study in a very precise way the significant application of the results for the existence of exact equilibrium solutions in ferromagnetics.
reviewed by: Elvira Mascolo
Mathematics Subject Classification ID: 35D99
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 1756807
MaRDI profile type: Publication
full work available at URL: s005260100092
OpenAlex ID: W1483268223
DOI: 10.1007/S005260100092
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description: scientific article; zbMATH DE number 1756807