{
  "id": "2206.11609",
  "version": "v1",
  "published": "2022-06-23T10:36:48.000Z",
  "updated": "2022-06-23T10:36:48.000Z",
  "title": "Estimates for Robin $p$-Laplacian eigenvalues of convex sets with prescribed perimeter",
  "authors": [
    "Vincenzo Amato",
    "Andrea Gentile",
    "Alba Lia Masiello"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we prove an upper bound for the first Robin eigenvalue of the $p$-Laplacian with a positive boundary parameter and a quantitative version of the reverse Faber-Krahn type inequality for the first Robin eigenvalue of the $p$-Laplacian with negative boundary parameter, among convex sets with prescribed perimeter. The proofs are based on a comparison argument obtained by means of inner sets, introduced by Payne, Weimberger and Polya.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-23T10:36:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "35A23",
      "35J92"
    ],
    "keywords": [
      "convex sets",
      "prescribed perimeter",
      "laplacian eigenvalues",
      "first robin eigenvalue",
      "boundary parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}