{
  "id": "1909.08122",
  "version": "v1",
  "published": "2019-09-17T21:50:45.000Z",
  "updated": "2019-09-17T21:50:45.000Z",
  "title": "Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities",
  "authors": [
    "Katya Krupchyk",
    "Gunther Uhlmann"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain $\\Omega\\subset \\mathbb{R}^n$ which vanish on a closed proper subset of the boundary is dense in $L^1(\\Omega)$. We apply this density result to solve some partial data inverse boundary problems for a class of semilinear elliptic PDE with quadratic gradient terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-17T21:50:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35J61"
    ],
    "keywords": [
      "partial data inverse problems",
      "semilinear elliptic equations",
      "gradient nonlinearities",
      "partial data inverse boundary problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}