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A lower bound for electrostatic capacity in the plane

Published online by Cambridge University Press:  14 November 2011

L. E. Fraenkel
L. E. Fraenkel
Affiliation:
Mathematics Division, University of Sussex
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Synopsis

This note presents a lower bound, in terms of the diameter ratio of the inner and outer conductors, for the electrostatic capacity of certain two-dimensional condensers. We use double Steiner symmetrization to prove that the minimizing condenser consists of a line segment placed symmetrically within a circle; the capacity of this condenser is known explicitly.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 3-4 , 1981 , pp. 267 - 273
Copyright
Copyright © Royal Society of Edinburgh 1981

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