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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
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.
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
Linking options:
https://www.mathnet.ru/eng/semr965 https://www.mathnet.ru/eng/semr/v15/p906
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Abstract page: | 185 | Full-text PDF : | 42 | References: | 20 |
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