Local behavior of p-harmonic Green's functions in metric 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 Poincaré inequality.

Cited by in corpus (7)

• Local and semilocal Poincaré inequalities on metric spaces
• Sharp capacity estimates for annuli in weighted R^n and in metric spaces
• Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces
• Locally $p$-admissible measures on $\mathbb{R}$
• Existence and almost uniqueness for $p$-harmonic Green functions on bounded domains in metric spaces
• Volume growth, capacity estimates, $p$-parabolicity and sharp integrability properties of $p$-harmonic Green functions
• Condenser capacities and capacitary potentials for unbounded sets, and global $p$-harmonic Green functions on metric spaces