{
  "id": "1811.08623",
  "version": "v2",
  "published": "2018-11-21T08:09:11.000Z",
  "updated": "2019-02-10T20:45:38.000Z",
  "title": "Non-solvability in the flat category of elliptic operators with real analytic coefficients",
  "authors": [
    "Martino Fassina",
    "Yifei Pan"
  ],
  "comment": "v2: material reorganized, exposition improved, Section 5 added. 18 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega\\subset\\mathbb{R}^n, n\\geq 2$, be an open set. For an elliptic differential operator $L$ on $\\Omega$ with real analytic coefficients and a point $p\\in\\Omega$, we construct a smooth function $g$ with the following properties: $g$ is flat at $p$ and the equation $Lu=g$ has no smooth local solution $u$ that is flat at $p$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-02-10T20:45:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J99",
      "32W99"
    ],
    "keywords": [
      "real analytic coefficients",
      "elliptic operators",
      "flat category",
      "non-solvability",
      "elliptic differential operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}