{
  "id": "1903.08118",
  "version": "v1",
  "published": "2019-03-19T17:21:38.000Z",
  "updated": "2019-03-19T17:21:38.000Z",
  "title": "Recovery of non-smooth coefficients appearing in anisotropic wave equations",
  "authors": [
    "Ali Feizmohammadi",
    "Yavar Kian"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the problem of unique recovery of a non-smooth one-form $\\mathcal A$ and a scalar function $q$ from the Dirichlet to Neumann map, $\\Lambda_{\\mathcal A,q}$, of a hyperbolic equation on a Riemannian manifold $(M,g)$. We prove uniqueness of the one-form $\\mathcal A$ up to the natural gauge, under weak regularity conditions on $\\mathcal A,q$ and under the assumption that $(M,g)$ is simple. Under an additional regularity assumption, we also derive uniqueness of the scalar function $q$. The proof is based on the geometric optic construction and inversion of the light ray transform extended as a Fourier Integral Operator to non-smooth parameters and functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-19T17:21:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anisotropic wave equations",
      "non-smooth coefficients appearing",
      "scalar function",
      "weak regularity conditions",
      "additional regularity assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}