Fractional Sobolev norms and BV functions on manifolds. (October 2019)

• Record Type: Journal Article
• Authors: Kreuml, Andreas; Mordhorst, Olaf
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 450
• Page End: 466
• Publication Date: 2019-10
• Subjects: Fractional Sobolev norms -- BV functions -- Sets of finite perimeter -- s-perimeter -- Non-local functionals; 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.2019.06.014
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on compact manifolds. As an application the special case of sets of finite perimeter is considered.