{
  "id": "1605.02363",
  "version": "v1",
  "published": "2016-05-08T20:17:56.000Z",
  "updated": "2016-05-08T20:17:56.000Z",
  "title": "Quantitative uniqueness for elliptic equations at the boundary of $C^{1, Dini}$ domains",
  "authors": [
    "Agnid Banerjee",
    "Nicola Garofalo"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Based on a variant of the frequency function approach of Almgren, we establish an optimal upper bound on the vanishing order of solutions to variable coefficient Schr\\\"odinger equations at a portion of the boundary of a $C^{1,Dini}$ domain. Such bound provides a quantitative form of strong unique continuation at the boundary. It can be thought of as a boundary analogue of an interior result recently obtained by Bakri and Zhu for the standard Laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-08T20:17:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic equations",
      "quantitative uniqueness",
      "optimal upper bound",
      "strong unique continuation",
      "frequency function approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}