{
  "id": "1711.03215",
  "version": "v1",
  "published": "2017-11-09T00:07:02.000Z",
  "updated": "2017-11-09T00:07:02.000Z",
  "title": "A gluing construction for fractional elliptic equations. Part I: a model problem on the catenoid",
  "authors": [
    "Hardy Chan",
    "Yong Liu",
    "Juncheng Wei"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We develop a new infinite dimensional gluing method for fractional elliptic equations. In Part I, as a model problem, we construct a solution of the fractional Allen--Cahn equation vanishing on a rotationally symmetric surface which resembles a catenoid and has sub-linear growth at infinity. In Part II, we construct counter-examples to De Giorgi Conjecture for the fractional Allen--Cahn equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-09T00:07:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional elliptic equations",
      "model problem",
      "gluing construction",
      "infinite dimensional gluing method",
      "fractional allen-cahn equation vanishing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}