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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 906–926 (Mi semr965)  

Real, complex and functional analysis

Approximate calculation of the defect of a Lipschitz cylindrical condenser

A. I. Parfenov

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: We introduce the notion of defect of a Lipschitz cylindrical condenser. It is the difference between the capacity of the condenser and its Ahlfors integral. We calculate the defect approximately for condensers over arbitrary open sets. For a condenser over an inner uniform domain the quantity obtained is comparable to the sum of the squares of the seminorms of the plates in a weighted homogeneous Slobodetskii space. This uses the characterization of inner uniform domains by the following property: every inner metric ball is a centered John domain.

Keywords: Ahlfors integral, capacity, condenser, defect, inner uniform domain, Lipschitz domain.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-5913.2018.1


DOI: https://doi.org/10.17377/semi.2018.15.078

Full text: PDF file (246 kB)
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Bibliographic databases:

Document Type: Article
UDC: 517.518
MSC: 31B15
Received July 6, 2018, published August 17, 2018

Citation: A. I. Parfenov, “Approximate calculation of the defect of a Lipschitz cylindrical condenser”, Sib. Èlektron. Mat. Izv., 15 (2018), 906–926

Citation in format AMSBIB
\Bibitem{Par18}
\by A.~I.~Parfenov
\paper Approximate calculation of the defect of a Lipschitz cylindrical condenser
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 906--926
\mathnet{http://mi.mathnet.ru/semr965}
\crossref{https://doi.org/10.17377/semi.2018.15.078}


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