Semicontinuité des fonctionnelles intégrales
type: Item
instance of: scholarly article
title: Semicontinuité des fonctionnelles intégrales
zbMATH Open document ID: 0557.49005
author: Paulette Clauzure
author: C. Castaing
published in: Acta Mathematica Vietnamica
publication date: 1984-01-01T00:00:00Z
review text: The problems of lower semicontinuity of integral functionals in general multidimensional setting are studied. Namely, the functionals of the form \(I(u,v)=\int_{T}f(t,u(t),v(t))\mu (dt)\) are considered, where, for instance, (T,\(\mu)\) is a compact metrizable space supplied with a Radon positive measure, the integrand \(f:T\times F\times E\to [0,+\infty]\) is approximatively semicontinuous, F is a Suslin locally convex space and E is a Suslin space. Several general theorems concerning lower semicontinuity and some specifications of these theorems are given. For instance, it is proved that under suitable assumptions \(\lim \inf_{n\to \infty}I(u_ n,v_ n)\geq I(u_ 0,v_ 0),\) when \(u_ n\to u_ 0\) in the weak topology \(\sigma (L_ F,L_{F'})\) and \(v_ n\) converges to a function \(v_ 0\) pointwise or in measure. The methods applied for getting such kind of theorems are those of the theory of duality of convex integrals and approximation of convex normal integrands by more regular ones.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49K27
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 46A03
zbMATH DE Number: 3888398
zbMATH Keywords: lower semicontinuity of integral functionals
zbMATH Keywords: Suslin space
zbMATH Keywords: duality of convex integrals
zbMATH Keywords: convex normal integrands
reviewed by: Zdzisław Denkowski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3888398