On Blaschke-Santalo diagrams for the torsional rigidity and the first Dirichlet eigenvalue

被引：10

作者：

Lucardesi, Ilaria ^{[1
]}

Zucco, Davide ^{[2
]}

机构：

[1] Univ Lorraine, CNRS, IECL, F-54000 Nancy, France

[2] Univ Torino, Dipartimento Matemat Giuseppe Peano, Via Carlo Alberto 10, I-10123 Turin, Italy

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2022年 / 201卷 / 01期

关键词：

Shape optimization; Blaschke– Santaló diagram; Torsional rigidity; First Dirichlet eigenvalue; BESSEL;

D O I：

10.1007/s10231-021-01113-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study Blaschke-Santalo 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.

引用

页码：175 / 201

页数：27

共 27 条

[21] Dual variational formulas for the first Dirichlet eigenvalue on half-line
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