Variational solutions to the total variation flow on metric measure spaces. (July 2022)

• Record Type: Journal Article
• Authors: Buffa, Vito; Kinnunen, Juha; Camacho, Cintia Pacchiano
• Is Part Of: Nonlinear analysis. Volume 220(2022)
• Publication Date: 2022-07
• Subjects: primary 30L99 35K99 -- secondary 35A15 49J27 49N60; Parabolic variational problems -- Time mollifications -- Metric measure spaces -- Sobolev spaces -- Parabolic 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.2022.112859
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincaré inequality. We apply the concept of parabolic De Giorgi classes together with upper gradients, Newtonian spaces and functions of bounded variation to prove a necessary and sufficient condition for a variational solution to be continuous at a given point.