Isoperimetric Inequalities in the Torsion and Clamped Membrane Problems for Convex Plane Domains

Abstract

Bounds for the curvature of the level curve of the torsion function through an arbitrary point in a convex region D, are used to derive improved isoperimetric inequalities for maximum stress, the torsional rigidity and other functionals. These inequalities are exact if D is either a circle or an infinite strip. A similar procedure is used in the clamped membrane problem, and again improved isoperimetric inequalities are derived.