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Matematicheskie Zametki, 2018, Volume 103, Issue 6, Pages 841–852
DOI: https://doi.org/10.4213/mzm11676 (Mi mzm11676) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On a Problem of Dubinin for the Capacity of a Condenser with a Finite Number of Plates

Yu. V. Dymchenkoa, V. A. Shlykb

a Far Eastern Federal University, Vladivostok
b Vladivostok Branch of Russian Customs Academy
Full-text PDF (495 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm11676
Abstract: It is proved that, in Euclidean $n$-space, $n\ge 2$, the weighted capacity (with Muckenhoupt weight) of a condenser with a finite number of plates is equal to the weighted modulus of the corresponding configuration of finitely many families of curves. For $n=2$, in the conformal case, this equality solves a problem posed by Dubinin.
Keywords: capacity of a condenser, Muckenhoupt weight, generalized condenser, modulus of a configuration.
Received: 16.05.2017
Revised: 19.07.2017
English version:
Mathematical Notes, 2018, Volume 103, Issue 6, Pages 901–910
DOI: https://doi.org/10.1134/S0001434618050267
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: Yu. V. Dymchenko, V. A. Shlyk, “On a Problem of Dubinin for the Capacity of a Condenser with a Finite Number of Plates”, Mat. Zametki, 103:6 (2018), 841–852; Math. Notes, 103:6 (2018), 901–910
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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