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Generalized capacities and polyhedral surfaces

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In the paper, the theory of extremal length of vector measures is used to show that the generalized condenser capacity in the sense of Aikawa and Ohtsuka is related to the module of the family of surfaces separating the condenser’s plates and disjoint with a given set. It is proved that the system of polyhedral surfaces from the above family is sufficient for approximating the module of this family. Bibliography: 17 titles.

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Authors and Affiliations

  1. Vladivostock Department of the Russian Customs Academy, Vladivostock, Russia

    P. A. Pugach

  2. Far-Eastern State University, Vladivostock, Russia

    V. A. Shlyk

Authors
  1. P. A. Pugach
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  2. V. A. Shlyk
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Correspondence to P. A. Pugach.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 383, 2010, pp. 148–178.

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Pugach, P.A., Shlyk, V.A. Generalized capacities and polyhedral surfaces. J Math Sci 178, 201–218 (2011). https://doi.org/10.1007/s10958-011-0540-2

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