{
  "id": "1610.01715",
  "version": "v1",
  "published": "2016-10-06T02:02:52.000Z",
  "updated": "2016-10-06T02:02:52.000Z",
  "title": "The $L^p$ Carleman estimate and a partial data inverse problem",
  "authors": [
    "Francis J. Chung",
    "Leo Tzou"
  ],
  "comment": "33 pages plus appendix and references",
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct an explicit Green's function for the conjugated Laplacian $e^{-\\omega \\cdot x/h}\\Delta e^{-\\omega \\cdot x/h}$, which let us control our solutions on roughly half of the boundary. We apply the Green's function to solve a partial data inverse problem for the Schr\\\"odinger equation with potential $q \\in L^{n/2}$. We also use this Green's function to derive $L^p$ Carleman estimates similar to the ones in Kenig-Ruiz-Sogge \\cite{krs}, but for functions with support up to part of the boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-06T02:02:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30"
    ],
    "keywords": [
      "partial data inverse problem",
      "carleman estimates similar",
      "explicit greens function",
      "roughly half"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}