Geodesic
A generalization of the Polia--Szego and Makai inequalities for torsional rigidity
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2021), pp. 86-91.

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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, distance to the boundary of domain.
Mots-clés : convex domains 
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L. I. Gafiyatullina; R. G. Salakhudinov. A generalization of the Polia--Szego and Makai inequalities for torsional rigidity. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2021), pp. 86-91. http://geodesic.mathdoc.fr/item/IVM_2021_11_a7/

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