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arXiv · 1701.05821

Optimal concavity of the torsion function

A. Henrot·C. Nitsch·P. Salani·C. Trombetti
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Abstract

In this short note we consider an unconventional overdetermined problem for the torsion function: let $n\geq 2$ and $Ω$ be a bounded open set in $\mathbb{R}^n$ whose torsion function $u$ (i.e. the solution to $Δu=-1$ in $Ω$, vanishing on $\partialΩ$) satisfies the following property: $\sqrt{M-u(x)}$ is convex, where $M=\max\{u(x)\,:\,x\in\overlineΩ\}$. Then $Ω$ is an ellipsoid.

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A. Henrot, C. Nitsch, P. Salani, C. Trombetti. 2017-01-20. Optimal concavity of the torsion function. https://arxiv.org/abs/1701.05821

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