{
  "id": "2212.05375",
  "version": "v1",
  "published": "2022-12-10T23:11:01.000Z",
  "updated": "2022-12-10T23:11:01.000Z",
  "title": "On a reverse Kohler-Jobin inequality",
  "authors": [
    "Luca Briani",
    "Giuseppe Buttazzo",
    "Serena Guarino Lo Bianco"
  ],
  "categories": [
    "math.OC",
    "math.AP"
  ],
  "abstract": "We consider the shape optimization problems for the quantities $\\lambda(\\Omega)T^q(\\Omega)$, where $\\Omega$ varies among open sets of $\\mathbb{R}^d$ with a prescribed Lebesgue measure. While the characterization of the infimum is completely clear, the same does not happen for the maximization in the case $q>1$. We prove that for $q$ large enough a maximizing domain exists among quasi-open sets and that the ball is optimal among {\\it nearly spherical domains}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-10T23:11:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reverse kohler-jobin inequality",
      "shape optimization problems",
      "prescribed lebesgue measure",
      "quasi-open sets",
      "quantities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}