{
  "id": "2109.14936",
  "version": "v2",
  "published": "2021-09-30T09:07:22.000Z",
  "updated": "2022-03-21T14:46:42.000Z",
  "title": "Sharp and quantitative estimates for the $p-$Torsion of convex sets",
  "authors": [
    "Vincenzo Amato",
    "Alba Lia Masiello",
    "Gloria Paoli",
    "Rossano Sannipoli"
  ],
  "comment": "17 pages, 4 figures",
  "categories": [
    "math.AP"
  ],
  "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 $.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-03-21T14:46:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "35J05",
      "35J25",
      "49Q10",
      "47J10"
    ],
    "keywords": [
      "convex set",
      "quantitative estimates",
      "polya type lower bound",
      "dirichlet boundary conditions",
      "planar case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}