{
  "id": "2003.11185",
  "version": "v1",
  "published": "2020-03-25T02:24:50.000Z",
  "updated": "2020-03-25T02:24:50.000Z",
  "title": "Green's function for nondivergence elliptic operators in two dimensions",
  "authors": [
    "Hongjie Dong",
    "Seick Kim"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct the Green function for second-order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition and the domain has $C^{1,1}$ boundary. We show that the Green's function is BMO in the domain and establish logarithmic pointwise bounds. We also obtain pointwise bounds for first and second derivatives of the Green's function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-25T02:24:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J08",
      "42B37"
    ],
    "keywords": [
      "greens function",
      "nondivergence elliptic operators",
      "dimensions",
      "second-order elliptic equations",
      "second derivatives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}