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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 906–926
DOI: https://doi.org/10.17377/semi.2018.15.078
(Mi semr965)
 

This article is cited in 1 scientific paper (total in 1 paper)

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
Full-text PDF (246 kB) Citations (1)
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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
Received July 6, 2018, published August 17, 2018
Bibliographic databases:
Document Type: Article
UDC: 517.518
MSC: 31B15
Language: Russian
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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  • This publication is cited in the following 1 articles:
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