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 
@article{IVM_2021_11_a7,
     author = {L. I. Gafiyatullina and R. G. Salakhudinov},
     title = {A generalization of the {Polia--Szego} and {Makai} inequalities for torsional rigidity},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--91},
     publisher = {mathdoc},
     number = {11},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_11_a7/}
}
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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/