Capacity of shrinking condensers in the plane

TL;DR

This paper investigates the capacity behavior of a specific class of plane condensers, demonstrating their capacity's comparability to dyadic condensers and revealing the unbounded growth as the plates approach each other.

Contribution

It establishes a comparison between the capacities of certain plane condensers and dyadic condensers, and shows the capacity's blow-up without an asymptotic estimate.

Findings

Capacity of the class of plane condensers is comparable to that of dyadic condensers.

Capacity blows up as the distance between plates shrinks.

No asymptotic estimate exists for the blow-up of capacity.

Abstract

We show that the capacity of a class of plane condensers is comparable to the capacity of corresponding "dyadic condensers". As an application, we show that for plane condensers in that class the capacity blows up as the distance between the plates shrinks, but there can be no asymptotic estimate of the blow-up.