{
  "id": "1903.10275",
  "version": "v1",
  "published": "2019-03-25T12:46:39.000Z",
  "updated": "2019-03-25T12:46:39.000Z",
  "title": "A Paneitz-Branson type equation with Neumann boundary conditions",
  "authors": [
    "Denis Bonheure",
    "Hussein Cheikh Ali",
    "Robson Nascimento"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the best constant in a critical Sobolev inequality of second order. We show non-rigidity for the optimizers above a certain treshold, namely we prove that the best constant is achieved by a non-constant solution of the associated fourth-order elliptic problem under Neumann boundary conditions. Our arguments rely on asymptotic estimates of the Rayleigh quotient. We also show rigidity below another treshold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-25T12:46:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neumann boundary conditions",
      "paneitz-branson type equation",
      "best constant",
      "associated fourth-order elliptic problem",
      "second order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}