Isoperimetric Inequalities in the Torsion and Clamped Membrane Problems for Convex Plane Domains
Isoperimetric Inequalities in the Torsion and Clamped Membrane Problems for Convex Plane Domains
复制标题
凸平面域扭转和夹紧膜问题中的等周不等式
DOI：
10.1137/0514089
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发表时间：
1983
影响因子：
2
通讯作者：
G. Philippin
中科院分区：
文献类型：
--
作者：
L. Payne;G. Philippin
通过凸区域D中任意一点的挠函数的水平曲线的曲率的界被用于导出最大应力、扭转刚度和其它泛函的改进的等周不等式。这些不等式是精确的，如果D是一个圆或一个无限的带。类似的过程中使用的固定膜问题，并再次改进等周不等式推导。
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.