{
  "id": "1604.01601",
  "version": "v1",
  "published": "2016-04-06T13:07:25.000Z",
  "updated": "2016-04-06T13:07:25.000Z",
  "title": "Inverse obstacle scattering with non-over-determined data",
  "authors": [
    "A. G. Ramm"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is proved that the scattering amplitude $A(\\beta, \\alpha_0, k_0)$, known for all $\\beta\\in S^2$, where $S^2$ is the unit sphere in $\\mathbb{R}^3$, and fixed $\\alpha_0\\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the obstacle $D$ and the boundary condition on $S$. The boundary condition on $S$ is assumed to be the Dirichlet, or Neumann, or the impedance one. The uniqueness theorem for the solution of multidimensional inverse scattering problems with non-over-determined data was not known for many decades. Such a theorem is proved in this paper for inverse scattering by obstacles for the first time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-06T13:07:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35J05"
    ],
    "keywords": [
      "inverse obstacle scattering",
      "non-over-determined data",
      "boundary condition",
      "multidimensional inverse scattering problems",
      "unit sphere"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160401601R"
    }
  }
}