{
  "id": "1305.2312",
  "version": "v2",
  "published": "2013-05-10T11:28:17.000Z",
  "updated": "2013-10-11T13:13:34.000Z",
  "title": "Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type",
  "authors": [
    "Barbara Brandolini",
    "Nunzia Gavitone",
    "Carlo Nitsch",
    "Cristina Trombetti"
  ],
  "comment": "Title change. Few typos",
  "categories": [
    "math.AP"
  ],
  "abstract": "The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-11T13:13:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35N25",
      "35B50",
      "35J60"
    ],
    "keywords": [
      "overdetermined boundary value problem",
      "monge-ampère type",
      "fully nonlinear boundary value problem",
      "non standard boundary conditions",
      "ellipsoids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2312B"
    }
  }
}