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Sibirsk. Mat. Zh., 2008, Volume 49, Number 5, Pages 1128–1146 (Mi smj1908)  

This article is cited in 6 scientific papers (total in 6 papers)

Variations of Robin capacity and applications

S. R. Nasyrov

Kazan State University, Faculty of Mechanics and Mathematics

Abstract: We obtain some estimates for the distortions of the moduli of quadrilaterals, the reduced moduli, and Robin capacities depending on the variation of the boundary of a domain. We show that for sufficiently smooth variations of the boundary the corresponding variations of the moduli and capacities are proportional to the area of the variable part of the domain in some extremal metric. We apply these results to studying the generalized Lavrent'ev problem of finding the shape of an infinitely thin airfoil of given length with the maximal aerodynamical lift under some restriction on the curvature of the airfoil.

Keywords: Robin capacity, moduli of quadrilaterals, extremal length of a family of curves, aerodynamical lift.

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English version:
Siberian Mathematical Journal, 2008, 49:5, 894–910

Bibliographic databases:

UDC: 517.54+532.5
Received: 06.09.2006

Citation: S. R. Nasyrov, “Variations of Robin capacity and applications”, Sibirsk. Mat. Zh., 49:5 (2008), 1128–1146; Siberian Math. J., 49:5 (2008), 894–910

Citation in format AMSBIB
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\pages 1128--1146
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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. V. V. Aseev, “Convex expansion of condenser plates”, Russian Math. (Iz. VUZ), 54:8 (2010), 1–11  mathnet  crossref  mathscinet  elib
    2. E. G. Prilepkina, “On composition principles for reduced moduli”, Siberian Math. J., 52:6 (2011), 1079–1091  mathnet  crossref  mathscinet  isi
    3. A. I. Parfenov, “Otsenka pogreshnosti obobschennoi formuly M. A. Lavrenteva normoi drobnogo prostranstva Soboleva”, Sib. elektron. matem. izv., 10 (2013), 335–377  mathnet
    4. E. G. Prilepkina, “Transfinite diameter with respect to Neumann function”, J. Math. Sci. (N. Y.), 200:5 (2014), 605–613  mathnet  crossref
    5. V. N. Dubinin, “Asymptotic Behavior of the Capacity of a Condenser as Some of Its Plates Contract to Points”, Math. Notes, 96:2 (2014), 187–198  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. V. N. Dubinin, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892  mathnet  crossref  mathscinet  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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