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

Abstract

It is proved that, in Euclidean n-space, n ≥ 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.