{
  "id": "1102.3446",
  "version": "v1",
  "published": "2011-02-16T22:26:10.000Z",
  "updated": "2011-02-16T22:26:10.000Z",
  "title": "Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones",
  "authors": [
    "Frank Pacard",
    "Juncheng Wei"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we are interested in bounded, entire, solutions of the Allen-Cahn equation which are defined in Euclidean space and whose zero set is asymptotic to a given minimal cone. In particular, in dimension larger than or equal to 8, we prove the existence of stable solutions of the Allen-Cahn equation whose zero sets are not hyperplanes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-16T22:26:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "allen-cahn equation",
      "minimal cone",
      "stable solutions",
      "zero set",
      "dimension larger"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.3446P"
    }
  }
}