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Mat. Zametki, 2011, Volume 90, Issue 2, Pages 216–230 (Mi mz8744)  

This article is cited in 2 scientific papers (total in 2 papers)

Sufficiency of Polyhedral Surfaces in the Modulus Method and Removable Sets

Yu. V. Dymchenko, V. A. Shlyk

Far Eastern National University

Abstract: The sufficiency of a family of polyhedral surfaces for calculating the modulus of a family of surfaces separating the plates of a condenser in an open set is proved. Geometric properties of removable sets for this modulus are also determined.

Keywords: modulus of a family of surfaces, condenser, surface separating plates of a condenser, removable set for a modulus of a family of surfaces, polyhedral surface, Lebesgue and Hausdorff measure, Borel function, Hölder inequality

DOI: https://doi.org/10.4213/mzm8744

Full text: PDF file (552 kB)
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English version:
Mathematical Notes, 2011, 90:2, 204–217

Bibliographic databases:

UDC: 517.54
Received: 16.03.2010

Citation: Yu. V. Dymchenko, V. A. Shlyk, “Sufficiency of Polyhedral Surfaces in the Modulus Method and Removable Sets”, Mat. Zametki, 90:2 (2011), 216–230; Math. Notes, 90:2 (2011), 204–217

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm8744
  • http://mi.mathnet.ru/eng/mz/v90/i2/p216

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. A. Pugach, V. A. Shlyk, “Removable sets for the generalized module of surface's family”, J. Math. Sci. (N. Y.), 184:6 (2012), 755–769  mathnet  crossref
    2. P. A. Pugach, V. A. Shlyk, “Piecewise linear approximation and polyhedral surfaces”, J. Math. Sci. (N. Y.), 200:5 (2014), 617–623  mathnet  crossref
  • Математические заметки Mathematical Notes
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