Isoperimetric Inequalities in the Torsion and Clamped Membrane Problems for Convex Plane Domains
- 1 November 1983
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 14 (6) , 1154-1162
- https://doi.org/10.1137/0514089
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.Keywords
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