Conditions on integral functional implying validity of the theory of weak convergence
type: Item
instance of: scholarly article
title: Conditions on integral functional implying validity of the theory of weak convergence
zbMATH Open document ID: 1246.46044
DOI: 10.1134/S1064562411040259
published in: Doklady Mathematics
publication date: 2012-01-17T00:00:00Z
review text: In this Doklady paper the author announces four theorems which give conditions implying validity of the theory of weak convergence (lower semicontinuity, relaxation, convergence with a functional, lower semicontinuous envelope). As a main auxiliary result a characterization of L-gradient Young measures serves, which was already proved under special conditions by \textit{D. Kinderlehrer} and \textit{P. Pedregal} [J. Geom. Anal. 4, No. 1, 59--90 (1994; Zbl 0808.46046)].
reviewed by: Alfred Göpfert
Mathematics Subject Classification ID: 46G12
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 5998452
zbMATH Keywords: lower semicontinuity
zbMATH Keywords: relaxation
zbMATH Keywords: Young measure
zbMATH Keywords: intergral functional
zbMATH Keywords: weak convergence
zbMATH Keywords: Carathéodory condition
author: M. A. Sychev
MaRDI profile type: Publication
cites work: Semicontinuity problems in the calculus of variations
cites work: Young measure approach to characterization of behaviour of integral functionals on weakly convergent sequences by means of their integrands
cites work: A new approach to Young measure theory, relaxation and convergence in energy
cites work: Sets of lower semicontinuity and stability of integral functionals
cites work: Attainment and relaxation results in special classes of deformations
cites work: Gradient Young measures generated by sequences in Sobolev spaces
description: scientific article; zbMATH DE number 5998452