On relations between principal eigenvalue and torsional rigidity-Reference-Cited by-同舟云学术

On relations between principal eigenvalue and torsional rigidity

Published:2020-12-17 Issue:08 Volume:23 Page:
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

van den Berg Michiel¹,Buttazzo Giuseppe²,Pratelli Aldo²

Affiliation:

1. School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, UK

2. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy

Abstract

We consider the problem of minimizing or maximizing the quantity [Formula: see text] on the class of open sets of prescribed Lebesgue measure. Here [Formula: see text] is fixed, [Formula: see text] denotes the first eigenvalue of the Dirichlet Laplacian on [Formula: see text], while [Formula: see text] is the torsional rigidity of [Formula: see text]. The optimization problem above is considered in the class of all domains [Formula: see text], in the class of convex domains [Formula: see text], and in the class of thin domains. The full Blaschke–Santaló diagram for [Formula: see text] and [Formula: see text] is obtained in dimension one, while for higher dimensions we provide some bounds.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199720500935

Reference20 articles.

1. Boundary Harnack Principle for p-harmonic Functions in Smooth Euclidean Domains

2. Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in Rd

3. Asymptotics for the Expected Lifetime of Brownian Motion on Thin Domains in ℝ n

4. On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique

5. Variational Methods in Shape Optimization Problems

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