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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2018 Volume 103, Issue 6, Pages 841–852 (Mi mzm11676)

This article is cited 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

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.

UDC: 517.54

Received: 16.05.2017
Revised: 19.07.2017

DOI: 10.4213/mzm11676


 English version:
Mathematical Notes, 2018, 103:6, 901–910

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© Steklov Math. Inst. of RAS, 2025