{
  "id": "0909.3803",
  "version": "v1",
  "published": "2009-09-21T15:34:53.000Z",
  "updated": "2009-09-21T15:34:53.000Z",
  "title": "Regularity and uniqueness of the first eigenfunction for singular fully non linear operators",
  "authors": [
    "Isabeau Birindelli",
    "Francoise Demengel"
  ],
  "comment": "30 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article we prove that solutions of singular fully nonlinear partial differential equations are $C^{1,\\beta}$. We also prove the simplicity of the principal eigenvalues for the Dirichlet Problem associated to these operators using that regularity, a strict comparison principle and Sard's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-21T15:34:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35P30"
    ],
    "keywords": [
      "singular fully non linear operators",
      "nonlinear partial differential equations",
      "first eigenfunction",
      "fully nonlinear partial differential",
      "regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}