Capacity of shrinking condensers in the plane

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...

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Bibliographic Details
Published in:	Journal of functional analysis Vol. 263; no. 10; pp. 3102 - 3116
Main Author:	Arcozzi, Nicola
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.11.2012
Subjects:	Condenser capacity Potential theory on trees Two-dimensional potential theory Condenser capacity Two-dimensional potential theory Potential theory on trees
ISSN:	0022-1236, 1096-0783
Online Access:	Get full text
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Summary:	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.
ISSN:	0022-1236 1096-0783
DOI:	10.1016/j.jfa.2012.07.016