Perimeter as relaxed Minkowski content in metric measure spaces. (April 2017)

• Record Type: Journal Article
• Authors: Ambrosio, Luigi; Di Marino, Simone; Gigli, Nicola
• Is Part Of: Nonlinear analysis. Volume 153(2017)
• Page Start: 78
• Page End: 88
• Publication Date: 2017-04
• Subjects: Minkowski content -- Perimeter -- BV functions; 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.2016.03.010
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this note we prove that on general metric measure spaces the perimeter is equal to the relaxation of the Minkowski contents w.r.t. convergence in measure.