Attainment and relaxation results in special classes of deformations
type: Item
instance of: scholarly article
title: Attainment and relaxation results in special classes of deformations
zbMATH Open document ID: 1051.49009
published in: Calculus of Variations and Partial Differential Equations
publication date: 2004-09-22T00:00:00Z
review text: The paper deals with attainment and relaxation issues in variational problems of mathematical theory of elasticity. Minimization problems are considered for energy functionals in certain classes of deformations which allow a reduction to essentially scalar cases. Relaxation results are established for integrands bounded from below by a power function, with exponent exceeding the independent variables space dimension. Bounds from below are improved in the homogeneous case. The mathematical fact exploited to achieve such results is that the relaxation result holds for those Sobolev functions that are a.e. differentiable in the classical sense, independently on the growth of the integrand. In the homogeneous case, a condition is indicated which is both necessary and sufficient for the solvability of all boundary value minimization problems of Dirichlet type.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 2102092
zbMATH Keywords: relaxation problems
zbMATH Keywords: polyconvexity
zbMATH Keywords: elasticity theory
author: M. A. Sychev
MaRDI profile type: Publication
full work available at URL: s00526-003-0215-z
OpenAlex ID: W2041722443
DOI: 10.1007/S00526-003-0215-Z
description: scientific article; zbMATH DE number 2102092