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

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

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
\Bibitem{Nas08} \by S.~R.~Nasyrov \paper Variations of Robin capacity and applications \jour Sibirsk. Mat. Zh. \yr 2008 \vol 49 \issue 5 \pages 1128--1146 \mathnet{http://mi.mathnet.ru/smj1908} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2469059} \transl \jour Siberian Math. J. \yr 2008 \vol 49 \issue 5 \pages 894--910 \crossref{https://doi.org/10.1007/s11202-008-0088-7} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000259921800015} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-53649098437} 

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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
2. E. G. Prilepkina, “On composition principles for reduced moduli”, Siberian Math. J., 52:6 (2011), 1079–1091
3. A. I. Parfenov, “Otsenka pogreshnosti obobschennoi formuly M. A. Lavrenteva normoi drobnogo prostranstva Soboleva”, Sib. elektron. matem. izv., 10 (2013), 335–377
4. E. G. Prilepkina, “Transfinite diameter with respect to Neumann function”, J. Math. Sci. (N. Y.), 200:5 (2014), 605–613
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
6. V. N. Dubinin, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892
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