Capacities and 1-strict subsets in metric spaces. (March 2020)

• Record Type: Journal Article
• Authors: Lahti, Panu
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 30L99 -- 31E05 -- 26B30; Metric measure space -- Capacity -- Strict subset -- Fine topology -- Function of bounded variation -- Pointwise approximation; 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.2019.111695
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In a complete metric space that is equipped with a doubling measure and supports a Poincaré inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case p = 1 . Relying on the concept of fine topology, we give a characterization of those strict subsets that are also sets of finite perimeter, and then we apply this to the study of condensers as well as BV capacities. We also apply the theory to prove a pointwise approximation result for functions of bounded variation.