{
  "id": "1102.4022",
  "version": "v1",
  "published": "2011-02-19T20:43:17.000Z",
  "updated": "2011-02-19T20:43:17.000Z",
  "title": "Even Symmetry of Some Entire Solutions to the Allen-Cahn Equation in Two Dimensions",
  "authors": [
    "Changfeng Gui"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we prove even symmetry and monotonicity of certain solutions of Allen-Cahn equation in a half plane. We also show that entire solutions with {\\it finite Morse index} and {\\it four ends} must be evenly symmetric with respect to two orthogonal axes. A classification scheme of general entire solutions with {\\it finite Morse index} is also presented using energy quantization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-19T20:43:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J60",
      "35J91",
      "49Q05",
      "53A04"
    ],
    "keywords": [
      "allen-cahn equation",
      "finite morse index",
      "dimensions",
      "general entire solutions",
      "half plane"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2012.03.004",
      "journal": "Journal of Differential Equations",
      "year": 2012,
      "volume": 252,
      "number": 11,
      "pages": 5853
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JDE...252.5853G"
    }
  }
}