{
  "id": "1809.09272",
  "version": "v1",
  "published": "2018-09-25T00:52:36.000Z",
  "updated": "2018-09-25T00:52:36.000Z",
  "title": "Nachman's reconstruction for the Calderon problem with discontinuous conductivities",
  "authors": [
    "George Lytle",
    "Peter Perry",
    "Samuli Siltanen"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that Nachman's integral equations for the Calder\\'on problem, derived for conductivities in $W^{2,p}(\\Omega)$, still hold for $L^\\infty$ conductivities which are $1$ in a neighborhood of the boundary. We also prove convergence of scattering transforms for smooth approximations to the scattering transform of $L^\\infty$ conductivities. We rely on Astala-P\\\"aiv\\\"arinta's formulation of the Calder\\'on problem for a framework in which these convergence results make sense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-25T00:52:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35P25",
      "35J25",
      "30C62"
    ],
    "keywords": [
      "calderon problem",
      "nachmans reconstruction",
      "discontinuous conductivities",
      "nachmans integral equations",
      "scattering transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}