Inserted: 2 feb 2017
Last Updated: 20 nov 2017
Journal: ESAIM: COCV
In this paper we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we consider $T(\Omega)/(M(\Omega)
)$ and $M(\Omega)\lambda_1(\Omega)$, where $\Omega$ is a bounded open set of $\mathbb R^d$ with finite Lebesgue measure $
$, $M(\Omega)$ 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.