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Variations of Robin capacity and applications

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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.

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Correspondence to S. R. Nasyrov.

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Original Russian Text Copyright © 2008 Nasyrov S. R.

The author was supported by the Russian Foundation for Basic Research (Grants 08-01-00381 and 06-01-81019-Bel).

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Kazan. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 5, pp. 1128–1146, September–October, 2008.

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Nasyrov, S.R. Variations of Robin capacity and applications. Sib Math J 49, 894–910 (2008). https://doi.org/10.1007/s11202-008-0088-7

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  • DOI: https://doi.org/10.1007/s11202-008-0088-7

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