{
  "id": "1211.3074",
  "version": "v2",
  "published": "2012-11-13T18:51:50.000Z",
  "updated": "2013-02-01T05:27:44.000Z",
  "title": "An Eigenvalue problem for the Infinity-Laplacian",
  "authors": [
    "Tilak Bhattacharya",
    "Leonardo Marazzi"
  ],
  "comment": "36 pages Accepted to EJDE. Changes have been made to improve the exposition",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study an eigenvalue problem for the infinity-Laplacian on bounded domains. We prove the existence of the principal eigenvalue and a corresponding positive eigenfunction. The work also contains existence results when the parameter, in the equation, is less than the first eigenvalue. A comparison principle applicable to these problems is also proven. Some additional results are shown, in particular, that on star- shaped domains and on C^2 domains higher eigenfunctions change sign. When the domain is a ball, we prove that the first eigenfunction has one sign, radial principal eigenfunction exist and are unique up to scalar multiplication, and that there are infinitely many eigenvalues.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-01T05:27:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J70",
      "35P30"
    ],
    "keywords": [
      "eigenvalue problem",
      "infinity-laplacian",
      "domains higher eigenfunctions change sign",
      "radial principal eigenfunction",
      "contains existence results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.3074B"
    }
  }
}