Variational approach to the asymptotic mean-value property for the p-Laplacian on Carnot groups. (September 2020)

• Record Type: Journal Article
• Authors: Adamowicz, Tomasz; Kijowski, Antoni; Pinamonti, Andrea; Warhurst, Ben
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: primary 35H20 -- secondary 31E05 35R03 53C17; Asymptotic mean value property -- Carnot group -- Heisenberg group -- Lie algebra -- Lie group -- Mean value formula -- p-Laplace -- Viscosity solution; 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.2020.111893
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let 1 ≤ p ≤ ∞ . We provide an asymptotic characterization of continuous viscosity solutions u of the normalized p -Laplacian Δ p G N u = 0 in any Carnot group G .