Abstract
We establish some generalizations of the classical inequalities by Polya–Szego and Makai about torsional rigidity of convex domains. The main idea of the proof is in using an exact isoperimetric inequality for Euclidean moments of domains. This inequality has a wide class of extremal regions and is of independent interest.
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Communicated by S. R. Nasyrov.
Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 11, pp. 86–91.
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Gafiyatullina, L.I., Salakhudinov, R.G. A Generalization of the Polia–Szego and Makai Inequalities for Torsional Rigidity. Russ Math. 65, 76–80 (2021). https://doi.org/10.3103/S1066369X21110086
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DOI: https://doi.org/10.3103/S1066369X21110086