{
  "id": "2006.07192",
  "version": "v1",
  "published": "2020-06-12T13:54:49.000Z",
  "updated": "2020-06-12T13:54:49.000Z",
  "title": "Concavity properties of solutions to Robin problems",
  "authors": [
    "Graziano Crasta",
    "Ilaria Fragalà"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that the Robin ground state and the Robin torsion function are respectively log-concave and $\\frac{1}{2}$-concave on an uniformly convex domain $\\Omega\\subset \\mathbb{R}^N$ of class $\\mathcal{C}^m$, with $[m -\\frac{ N}{2}]\\geq 4$, provided the Robin parameter exceeds a critical threshold. Such threshold depends on $N$, $m$, and on the geometry of $\\Omega$, precisely on the diameter and on the boundary curvatures up to order $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-12T13:54:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35E10",
      "35B65",
      "35J15",
      "35J25"
    ],
    "keywords": [
      "robin problems",
      "concavity properties",
      "robin ground state",
      "robin torsion function",
      "robin parameter exceeds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}