Integral representation and relaxation of local functionals on Cheeger–Sobolev spaces. (April 2022)

• Record Type: Journal Article
• Authors: Anza Hafsa, Omar; Mandallena, Jean-Philippe
• Is Part Of: Nonlinear analysis. Volume 217(2022)
• Publication Date: 2022-04
• Subjects: Integral representation -- Relaxation -- Integral functionals defined on Cheeger–Sobolev spaces; 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.2021.112744
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove an integral representation theorem for local functionals with polynomial growth defined on Cheeger–Sobolev spaces. More precisely, we give a version of the well-known Buttazzo–Dal maso's integral representation theorem in the framework of Cheeger–Sobolev spaces. The integral representation theorem is used to prove a relaxation theorem.