{
  "id": "1511.01700",
  "version": "v1",
  "published": "2015-11-05T11:33:48.000Z",
  "updated": "2015-11-05T11:33:48.000Z",
  "title": "The Calderón problem is an inverse source problem",
  "authors": [
    "Jan Cristina"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that uniqueness for the Calder\\'on problem on a Riemannian manifold with boundary follows from a hypothetical unique continuation property for the elliptic operator $\\Delta+V+(\\Lambda^{1}_{t}-q)\\otimes (\\Lambda^{2}_{t}-q)$ defined on $\\partial\\mathcal{M}^{2}\\times [0,1]$ where $V$ and $q$ are potentials and $\\Lambda^{i}_{t}$ is a Dirichlet-Neumann operator at depth $t$. This is done by showing that the difference of two Dirichlet-Neumann maps is equal to the Neumann boundary values of the solution to an inhomogeneous equation for said operator, where the source term is a measure supported on the diagonal of $\\partial\\mathcal{M}^{2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-05T11:33:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35J25",
      "37L05",
      "58J05",
      "58J32"
    ],
    "keywords": [
      "inverse source problem",
      "calderón problem",
      "neumann boundary values",
      "hypothetical unique continuation property",
      "calderon problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151101700C"
    }
  }
}