Quasiadditivity of variational capacity

TL;DR

This paper investigates the quasiadditivity property of variational capacity in metric spaces, linking it to capacity conditions and Hardy's inequality, providing new insights into potential theory in these spaces.

Contribution

It characterizes quasiadditivity of variational capacity via a Mazya type capacity condition and explores its relationship with Hardy's inequality in metric spaces.

Findings

Quasiadditivity is characterized by a Mazya type capacity condition.

A close relation between quasiadditivity and Hardy's inequality is established.

The results enhance understanding of variational capacity in metric spaces.

Abstract

We study the quasiadditivity property (a version of superadditivity with a multiplicative constant) of variational capacity in metric spaces with respect to Whitney type covers. We characterize this property in terms of a Mazya type capacity condition, and also explore the close relation between quasiadditivity and Hardy's inequality.