Sharp capacitary estimates for rings in metric spaces

Abstract

We establish sharp estimates for the $p$-capacity of metric rings with unrelated radii in metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality. These estimates play an essential role in the study of the local behavior of \p-harmonic Green's functions.

Cited by in corpus (4)

• Prime ends for domains in metric spaces
• Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces
• Locally $p$-admissible measures on $\mathbb{R}$
• Volume growth, capacity estimates, $p$-parabolicity and sharp integrability properties of $p$-harmonic Green functions