{
  "id": "1702.01258",
  "version": "v1",
  "published": "2017-02-04T09:18:35.000Z",
  "updated": "2017-02-04T09:18:35.000Z",
  "title": "On two functionals involving the maximum of the torsion function",
  "authors": [
    "Antoine Henrot",
    "Ilaria Lucardesi",
    "Gérard Philippin"
  ],
  "categories": [
    "math.AP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-04T09:18:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "49R05",
      "35J25",
      "35B27",
      "49Q10"
    ],
    "keywords": [
      "torsion function",
      "first dirichlet eigenvalue",
      "finite lebesgue measure",
      "lower bounds",
      "shape functionals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}