On a problem of Dubinin for the capacity of a condenser with a finite number of plates. (English. Russian original) Zbl 1397.30025
Math. Notes 103, No. 6, 901-910 (2018); translation from Mat. Zametki 103, No. 6, 841-852 (2018).
Summary: It is proved that, in Euclidean \(n\)-space, \(n\geq2\), 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.
MSC:
| 30C75 | Extremal problems for conformal and quasiconformal mappings, other methods |
| 31B15 | Potentials and capacities, extremal length and related notions in higher dimensions |
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