Removable singularities for bounded A-(super)harmonic and quasi(super)harmonic functions on weighted Rn. (September 2022)

• Record Type: Journal Article
• Authors: Björn, Anders
• Is Part Of: Nonlinear analysis. Volume 222(2022)
• Publication Date: 2022-09
• Subjects: primary 31C45 -- secondary 31E05 35J92; A-harmonic function -- A-superharmonic function -- Bounded -- p-admissible weight -- p-harmonic function -- p-superharmonic function -- Quasiharmonic function -- Quasisuperharmonic function -- Removable singularity -- Weighted Euclidean space.; 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.2022.112907
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: It is well known that sets of p -capacity zero are removable for bounded p -harmonic functions, but on metric spaces there are examples of removable sets of positive capacity. In this paper, we show that this can happen even on unweighted R n when n > p, although only in very special cases. A complete characterization of removable singularities for bounded A -harmonic functions on weighted R n, n ≥ 1, is also given, where the weight is p -admissible. The same characterization is also shown to hold for bounded quasiharmonic functions on weighted R n, n ≥ 2, as well as on unweighted R . For bounded A -superharmonic functions and bounded quasisuperharmonic functions on weighted R n, n ≥ 2, we show that relatively closed sets are removable if and only if they have zero capacity.