A Generalization of the Polia–Szego and Makai Inequalities for Torsional Rigidity

Abstract

We establish some generalizations of theclassical inequalities by Polya–Szego and Makai about torsionalrigidity of convex domains. The main idea of the proof is in usingan exact isoperimetric inequality for Euclidean moments ofdomains. This inequality has a wide class of extremal regions andis of independent interest.