On coercive variational integrals. (April 2017)

• Record Type: Journal Article
• Authors: Chen, Chuei Yee; Kristensen, Jan
• Is Part Of: Nonlinear analysis. Volume 153(2017)
• Page Start: 213
• Page End: 229
• Publication Date: 2017-04
• Subjects: Coercivity -- Quasiconvexity -- Variational integral; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.09.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: It is well-known that sequential weak lower semicontinuity of a variational integral F ( u, Ω ) = ∫ Ω F ( ∇ u ( x ) ) d x on the Sobolev space W 1, p ( Ω, R N ) under a p –growth condition on the integrand F is equivalent to quasiconvexity in the sense of Morrey. We show that coercivity on Dirichlet classes likewise is equivalent to a quasiconvexity condition. We also discuss some examples and extend a sequential weak lower semicontinuity result to the case of signed integrands.