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Mat. Zametki, 2018, Volume 103, Issue 6, Pages 841–852 (Mi mz11676)  

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

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.

DOI: https://doi.org/10.4213/mzm11676

Full text: PDF file (495 kB)
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English version:
Mathematical Notes, 2018, 103:6, 901–910

Bibliographic databases:

Document Type: Article
UDC: 517.54
Received: 16.05.2017
Revised: 19.07.2017

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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