{
  "id": "1811.02845",
  "version": "v1",
  "published": "2018-11-07T11:43:13.000Z",
  "updated": "2018-11-07T11:43:13.000Z",
  "title": "An $L^\\infty$ regularisation strategy to the inverse source identification problem for elliptic equations",
  "authors": [
    "Nikos Katzourakis"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we utilise new methods of Calculus of Variations in $L^\\infty$ to provide a regularisation strategy to the ill-posed inverse problem of identifying the source of a non-homogeneous linear elliptic equation, satisfying Dirichlet data on a domain. One of the advantages over the classical Tykhonov regularisation in $L^2$ is that the approximated solution of the PDE is uniformly close to the noisy measurements taken on a compact subset of the domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-07T11:43:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse source identification problem",
      "regularisation strategy",
      "noisy measurements taken",
      "non-homogeneous linear elliptic equation",
      "compact subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}