Local behavior of p-harmonic Green's functions in metric spaces

TL;DR

This paper investigates the local behavior of p-harmonic Green's functions near singularities within metric measure spaces that have a doubling measure and support a Poincaré inequality, providing insights into their structure.

Contribution

It characterizes the local behavior of p-harmonic Green's functions in metric spaces with specific geometric and measure-theoretic properties, extending classical results.

Findings

Describes the asymptotic behavior near singularities

Provides conditions under which Green's functions exhibit specific local patterns

Extends understanding of p-harmonic functions in non-smooth spaces

Abstract

We describe the behavior of p-harmonic Green's functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincar\'e inequality.