A sharp attainment result for nonconvex variational problems
type: Item
instance of: scholarly article
title: A sharp attainment result for nonconvex variational problems
zbMATH Open document ID: 1058.49002
published in: Calculus of Variations and Partial Differential Equations
publication date: 2004-12-16T00:00:00Z
review text: The authors study the existence of solutions to problems of calculus of variations of the form: Minimize \(I(u)\) over the set \(u_0+ W_0^{1,p}(\Omega)\), where \(I(u) = \int_\Omega f(u(x),\nabla u(x))\,dx\), \(\Omega\) is an open bounded subset of \({\mathbb R}^N\), \(N\geq 2\), \(f: {\mathbb R}\times {\mathbb R}^N \mapsto [0,\infty)\) is a continuous function which can be nonconvex with respect to \(\nabla u\), and \(u_0\in W^{1,p}(\Omega)\). Existence results in the case when \(f\) is of the form \(f(u,\nabla u)=g(u)+h(\nabla u)\), with \(h\) nonconvex, have already been proved in the literature. The authors obtain new existence results in classes of functions \(f\) more general than the ones already considered in previous papers.
reviewed by: J-P Raymond
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 49K10
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 2123232
zbMATH Keywords: existence of minimizers
zbMATH Keywords: nonconvex variational problems
author: Pietro Celada
author: Giovanni Cupini
author: M. Guidorzi
MaRDI profile type: Publication
full work available at URL: s00526-003-0238-5
OpenAlex ID: W2062225637
DOI: 10.1007/S00526-003-0238-5
description: scientific article; zbMATH DE number 2123232