On formulae decoupling the total variation of BV functions. (May 2017)

• Record Type: Journal Article
• Authors: Ponce, Augusto C.; Spector, Daniel
• Is Part Of: Nonlinear analysis. Volume 154(2017)
• Page Start: 241
• Page End: 257
• Publication Date: 2017-05
• Subjects: Bounded variation -- Fractional Laplacian -- Non-local energies; 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.2016.08.028
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we prove several formulae that enable one to capture the singular portion of the measure derivative of a function of bounded variation as a limit of non-local functionals. One special case shows that rescalings of the fractional Laplacian of a function u ∈ S B V converge strictly to the singular portion of D u .