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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 11, Pages 86–91
DOI: https://doi.org/10.26907/0021-3446-2021-11-86-91 (Mi ivm9731) 		 
Brief communications

A generalization of the Polia–Szego and Makai inequalities for torsional rigidity

L. I. Gafiyatullina, R. G. Salakhudinov

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
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DOI: https://doi.org/10.26907/0021-3446-2021-11-86-91
Abstract: We prove generalizations of the classical inequalities of Polia — Szegо and Makai about torsional rigidity of convex domains. The main idea of the proof is to apply an exact isoperimetric inequality of for Euclidean moments of a domain. This inequality has a wide class of extremal regions and is of independent interest.
Keywords: torsional rigidity, Euclidean moments of the domain with respect to its boundary, isoperimetric inequalities, convex domains, distance to the boundary of domain.
Received: 15.07.2021
Revised: 15.07.2021
Accepted: 29.09.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 11, Pages 76–80
DOI: https://doi.org/10.3103/S1066369X21110086
Document Type: Article
UDC: 514.763
Language: Russian
Citation: L. I. Gafiyatullina, R. G. Salakhudinov, “A generalization of the Polia–Szego and Makai inequalities for torsional rigidity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 11, 86–91; Russian Math. (Iz. VUZ), 65:11 (2021), 76–80
Citation in format AMSBIB
\Bibitem{GafSal21}
\by L.~I.~Gafiyatullina, R.~G.~Salakhudinov
\paper A generalization of the Polia--Szego and Makai inequalities for torsional rigidity
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 11
\pages 86--91
\mathnet{http://mi.mathnet.ru/ivm9731}
\crossref{https://doi.org/10.26907/0021-3446-2021-11-86-91}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2021
\vol 65
\issue 11
\pages 76--80
\crossref{https://doi.org/10.3103/S1066369X21110086}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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