# On two functionals involving the maximum of the torsion function

created by lucardesi on 02 Feb 2017
modified on 20 Nov 2017

[BibTeX]

Accepted Paper

Inserted: 2 feb 2017
Last Updated: 20 nov 2017

Journal: ESAIM: COCV
Year: 2017
Doi: https://doi.org/10.1051/cocv/2017069

Abstract:

In this paper we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we consider $T(\Omega)/(M(\Omega) \Omega )$ and $M(\Omega)\lambda_1(\Omega)$, where $\Omega$ is a bounded open set of $\mathbb R^d$ with finite Lebesgue measure $\Omega$, $M(\Omega)$ denotes the maximum of the torsion function, $T(\Omega)$ the torsion, and $\lambda_1(\Omega)$ the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets.