Existence of scalar minimizers for nonconvex simple integrals of sum type
type: Item
instance of: scholarly article
title: Existence of scalar minimizers for nonconvex simple integrals of sum type
zbMATH Open document ID: 0920.49026
author: António Ornelas
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-08-15T00:00:00Z
review text: The paper deals with an existence result for a Lagrange problem of the calculus of variations with a nonconvex Lagrangian. Specifically, it is proved that the problem \[ \min\biggl\{\int_0^1h(x'(t))+\varphi(x(t)) dt:\;x\in AC(0,1), x(0)=A, x(1)=B\biggr\} \] has at least one solution provided \(\varphi\) is a non negative lower semicontinuous function, \(h\) has a superlinear growth at infinity and \(h(0)=h^{**}(0)\), where \(h^{**}\) is the convex envelope of \(h\). The existence proof is obtained passing through the analysis of the relaxed variational problem, involving \(h^{**}\) in place of \(h\).
Mathematics Subject Classification ID: 49Q10
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 1217028
zbMATH Keywords: calculus of variations
zbMATH Keywords: nonconvex integrals
zbMATH Keywords: Lagrange problem
reviewed by: Luigi Ambrosio
MaRDI profile type: Publication
full work available at URL: jmaa.1998.5915
OpenAlex ID: W1978252484
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DOI: 10.1006/JMAA.1998.5915
description: scientific article; zbMATH DE number 1217028