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Ufa Mathematical Journal, 2024, Volume 16, Issue 3, Pages 21–39
DOI: https://doi.org/10.13108/2024-16-3-21 (Mi ufa699) 		 
Estimates for torsional rigidity of convex domain via new geometric characteristics

L. I. Gafiyatullina, R. G. Salakhudinov

Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kremlevskaya str. 35, 420008, Kazan, Russia
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DOI: https://doi.org/10.13108/2024-16-3-21
Abstract: We introduce new geometric characteristics of a convex domain with finite boundary length and provide an algorithm for calculating them. A series of isoperimetric inequalities between new functionals and known integral characteristics of the domain are proved. Some of the inequalities have a wide class of extremal domains. We consider applications of new characteristics to the problem on estimating the torsional rigidity of a convex domain.
Keywords: convex domain, function of distance to the boundary, torsional rigidity, isoperimetric inequality, extremal domain.
Received: 15.08.2023
Document Type: Article
UDC: 517.5
MSC: 26A99, 26D99, 30C99
Language: English
Original paper language: Russian
Citation: L. I. Gafiyatullina, R. G. Salakhudinov, “Estimates for torsional rigidity of convex domain via new geometric characteristics”, Ufa Math. J., 16:3 (2024), 21–39
Citation in format AMSBIB
\Bibitem{GafSal24}
\by L.~I.~Gafiyatullina, R.~G.~Salakhudinov
\paper Estimates for torsional rigidity of convex domain via new geometric characteristics
\jour Ufa Math. J.
\yr 2024
\vol 16
\issue 3
\pages 21--39
\mathnet{http://mi.mathnet.ru/eng/ufa699}
\crossref{https://doi.org/10.13108/2024-16-3-21}
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