Convergence of natural p-means for the p-Laplacian in the Heisenberg group. (October 2022)

• Record Type: Journal Article
• Authors: Domokos, András; Manfredi, Juan J.; Ricciotti, Diego; Stroffolini, Bianca
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: 35J92 -- 35D40 -- 49L20 -- 49L25 -- 35R02 -- 35B05 -- 35J62; p-Laplacian -- Natural p-means -- Dirichlet problem -- Discrete approximations -- Asymptotic mean value properties -- Convergence -- Generalized viscosity solutions -- Heisenberg group; 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.2022.113058
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we prove uniform convergence of approximations to p -harmonic functions by using natural p -mean operators on bounded domains of the Heisenberg group H which satisfy an intrinsic exterior corkscrew condition. These domains include Euclidean C 1, 1 domains.