A new approach to Young measure theory, relaxation and convergence in energy
type: Item
instance of: scholarly article
title: A new approach to Young measure theory, relaxation and convergence in energy
zbMATH Open document ID: 0943.49012
DOI: 10.1016/S0294-1449(00)88187-1
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2000-01-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78483
review text: The paper contains a detailed presentation of the theory of Young measures, with particular emphasis on their application to the study of lower semicontinuity of integral functionals of the calculus of variations of the form \[ I(u)= \int_\Omega L(x,u,\nabla u) dx.\tag{1} \] Section 2 deals with some properties of functions in Sobolev spaces. Section 3 is devoted to Young measures and to the characterization of them as measurable functions into a suitable metric space. In Section 4 the theory of gradient Young measures is presented together with a survey on the already existing literature. Section 5 finally deals with some applications of Young measures to the study of the asymptotic behaviour of integral functionals of the form (1) on weakly convergent sequences of Sobolev functions, which allows to obtain relaxation results under minimal assumptions on the integrand \(L\).
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 46E27
Mathematics Subject Classification ID: 34B20
zbMATH DE Number: 1394706
zbMATH Keywords: Young measures
zbMATH Keywords: lower semicontinuity
zbMATH Keywords: integral functionals
zbMATH Keywords: relaxation
author: M. A. Sychev
reviewed by: Giuseppe Buttazzo
MaRDI profile type: Publication
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OpenAlex ID: W1971927621
description: scientific article; zbMATH DE number 1394706