{
  "id": "1811.03506",
  "version": "v1",
  "published": "2018-11-08T15:48:43.000Z",
  "updated": "2018-11-08T15:48:43.000Z",
  "title": "Two estimates for the first Robin eigenvalue of the Finsler Laplacian with negative boundary parameter",
  "authors": [
    "Gloria Paoli",
    "Leonardo Trani"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove two bounds for the first Robin eigenvalue of the Finsler Laplacian with negative boundary parameter in the planar case. In the constant area problem, we show that the Wulff shape is the maximizer only for values which are close to 0 of the boundary parameter and, in the fixed perimeter case, that the Wulff shape maximizes the first eigenvalue for all values of the parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-08T15:48:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50",
      "35P15"
    ],
    "keywords": [
      "first robin eigenvalue",
      "negative boundary parameter",
      "finsler laplacian",
      "wulff shape maximizes",
      "constant area problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}