RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sib. Èlektron. Mat. Izv.: Year: Volume: Issue: Page: Find

 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 ÍØ-5913.2018.1

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

Full text: PDF file (246 kB)
References: PDF file   HTML file

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} `