{
  "id": "2206.04866",
  "version": "v1",
  "published": "2022-06-10T04:30:34.000Z",
  "updated": "2022-06-10T04:30:34.000Z",
  "title": "Determining an unbounded potential for an elliptic equation with power type nonlinearities",
  "authors": [
    "Janne Nurminen"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential $q$ in $L^{n/2+\\varepsilon}$, $\\varepsilon>0$, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the results from [M. Lassas, T. Liimatainen, Y.-H. Lin, and M. Salo, Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations, Rev. Mat. Iberoam. (2021)] where this is shown for H\\\"older continuous potentials. Also we show that when the Dirichlet-to-Neumann map is restricted to one point on the boundary, it is possible to determine a potential $q$ in $L^{n+\\varepsilon}$. The authors of arXiv:2202.05290 [math.AP] proved this to be true for H\\\"older continuous potentials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-10T04:30:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35J25",
      "35J61"
    ],
    "keywords": [
      "power type nonlinearities",
      "unbounded potential",
      "semilinear elliptic equation",
      "partial data inverse problems",
      "partial dirichlet-to-neumann map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}