On Blaschke–Santaló diagrams for the torsional rigidity and the first Dirichlet eigenvalue

被引：0
作者：
Ilaria Lucardesi
Davide Zucco
机构：
[1] Université de Lorraine,CNRS, IECL
[2] Università di Torino,Dipartimento di Matematica “Giuseppe Peano”
来源：
Annali di Matematica Pura ed Applicata (1923 -) | 2022年 / 201卷
关键词：
Shape optimization; Blaschke–Santaló diagram; Torsional rigidity; First Dirichlet eigenvalue; 49Q10; 49R05; 35P15; 35J25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study Blaschke–Santaló diagrams associated with the torsional rigidity and the first eigenvalue of the Laplacian with Dirichlet boundary conditions. We work under convexity and volume constraints, in both strong (volume exactly one) and weak (volume at most one) form. We discuss some topological (closedness, simply connectedness) and geometric (shape of the boundaries, slopes near the point corresponding to the ball) properties of these diagrams, also providing a list of conjectures.
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页码：175 / 201
页数：26
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