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arXiv · 1702.01258

On two functionals involving the maximum of the torsion function

Antoine Henrot·Ilaria Lucardesi·Gérard Philippin
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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.

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Antoine Henrot, Ilaria Lucardesi, Gérard Philippin. 2017-02-04. On two functionals involving the maximum of the torsion function. https://arxiv.org/abs/1702.01258

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