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Sharp and quantitative estimates for the $p-$Torsion of convex sets
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
Abstract
- Let $\Omega\subset\mathbb{R}^n$, $n\geq 2$, 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 $\Omega$. We consider the $p-$torsional rigidity associated to $\Omega$ for the Poisson problem with Dirichlet boundary conditions, denoted by $T_{f,p}(\Omega)$. Firstly, we prove a P\'olya type lower bound for $T_{f,p}(\Omega)$ in any dimension; then, we consider the planar case and we provide two quantitative estimates in the case $f\equiv 1 $.<br />Comment: 18 pages, 4 figures
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....6fa4cf5a422abfd2591118b189635f9b
- Full Text :
- https://doi.org/10.48550/arxiv.2109.14936