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arXiv · 2109.14936

Sharp and quantitative estimates for the $p-$Torsion of convex sets

Vincenzo Amato·Alba Lia Masiello·Gloria Paoli·Rossano Sannipoli
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Abstract

Let $Ω\subset\mathbb{R}^n$, $n\geq 2$, be a bounded, open and convex set and let $f$ be a positive and non-increasing function depending only on the distance from the boundary of $Ω$. We consider the $p-$torsional rigidity associated to $Ω$ for the Poisson problem with Dirichlet boundary conditions, denoted by $T_{f,p}(Ω)$. Firstly, we prove a Pólya type lower bound for $T_{f,p}(Ω)$ in any dimension; then, we consider the planar case and we provide two quantitative estimates in the case $f\equiv 1 $.

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Vincenzo Amato, Alba Lia Masiello, Gloria Paoli, Rossano Sannipoli. 2022-10-05. Sharp and quantitative estimates for the $p-$Torsion of convex sets. https://arxiv.org/abs/2109.14936

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