{
  "id": "2309.06446",
  "version": "v1",
  "published": "2023-09-12T00:49:29.000Z",
  "updated": "2023-09-12T00:49:29.000Z",
  "title": "Local Spectral Optimisation for Robin Problems with Negative Boundary Parameter on Quadrilaterals",
  "authors": [
    "Julie Clutterbuck",
    "James Larsen-Scott"
  ],
  "comment": "32 pages, 2 figures",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "We investigate the Robin eigenvalue problem for the Laplacian with negative boundary parameter on quadrilateral domains of fixed area. In this paper, we prove that the square is a local maximiser of the first eigenvalue with respect to the Hausdorff metric. We also provide asymptotic results relating to the optimality of the square for extreme values of the Robin parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-12T00:49:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "35J25",
      "35J05",
      "49R05"
    ],
    "keywords": [
      "negative boundary parameter",
      "local spectral optimisation",
      "robin problems",
      "robin eigenvalue problem",
      "extreme values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}