{
  "id": "2010.11409",
  "version": "v1",
  "published": "2020-10-21T07:43:35.000Z",
  "updated": "2020-10-21T07:43:35.000Z",
  "title": "Partial data inverse problems for quasilinear conductivity equations",
  "authors": [
    "Yavar Kian",
    "Katya Krupchyk",
    "Gunther Uhlmann"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1909.08122",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in $\\mathbb{R}^n$, $n\\ge 2$, for classes of semilinear and quasilinear conductivity equations, determines the nonlinear conductivities uniquely. The main ingredient in the proof is a certain $L^1$-density result involving sums of products of gradients of harmonic functions which vanish on a closed proper subset of the boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-21T07:43:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35J61"
    ],
    "keywords": [
      "partial data inverse problems",
      "quasilinear conductivity equations",
      "arbitrary open non-empty portion",
      "harmonic functions",
      "density result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}