On a new class of elastic deformations not allowing for cavitation
type: Item
instance of: scholarly article
title: On a new class of elastic deformations not allowing for cavitation
zbMATH Open document ID: 0863.49002
DOI: 10.1016/S0294-1449(16)30193-7
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1996-02-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78330
review text: The divergence identity \[ \partial_j\{(g^i\circ u)(\text{adj }Du)^j_i\}= (\text{div }g)\circ\text{det }Du \] is proved under weak assumptions. Also, an integrability result for \(\text{det }Du\) is proved. As an application, a degree formula is proved in the class \(A_{p,q}(\Omega)\). As a further application, the existence of an absolutely continuous minimizer of \[ I(u)=\int_\Omega W(x,u,Du)dx \] is proved if \(W\) is polyconvex and satisfies the inequality \(W(x,u,F)\geq a(|F|^p+|\text{adj }F|^q)\) with \(p\geq 2\) and \(q\geq 3/2\).
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 26B10
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 827004
zbMATH Keywords: nonlinear elasticity
zbMATH Keywords: divergence identity
zbMATH Keywords: degree formula
zbMATH Keywords: absolutely continuous minimizer
author: Stefan Müller
author: Qi Tang
author: Baisheng Yan
reviewed by: Martin Brokate
MaRDI profile type: Publication
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OpenAlex ID: W96040618
description: scientific article; zbMATH DE number 827004