{
  "id": "2401.06120",
  "version": "v1",
  "published": "2024-01-11T18:55:51.000Z",
  "updated": "2024-01-11T18:55:51.000Z",
  "title": "Reconstruction for the Calderón problem with Lipschitz conductivities",
  "authors": [
    "Pedro Caro",
    "María Ángeles García-Ferrero",
    "Keith M. Rogers"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We determine the conductivity of the interior of a body using electrical measurements on its surface. We assume only that the conductivity is bounded below by a positive constant and that the conductivity and surface are Lipschitz continuous. To determine the conductivity we first solve an associated integral equation locally, finding solutions in $H^1(B)$, where $B$ is a ball that properly contains the body. A key ingredient is to equip this Sobolev space with an equivalent norm which depends on two auxiliary parameters that can be chosen to yield a contraction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-11T18:55:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30"
    ],
    "keywords": [
      "conductivity",
      "calderón problem",
      "lipschitz conductivities",
      "reconstruction",
      "auxiliary parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}