{
  "id": "1112.2441",
  "version": "v1",
  "published": "2011-12-12T04:57:45.000Z",
  "updated": "2011-12-12T04:57:45.000Z",
  "title": "Sharp estimates for the Neumann functions and applications to quantitative photo-acoustic imaging in inhomogeneous media",
  "authors": [
    "Habib Ammari",
    "Hyeonbae Kang",
    "Seick Kim"
  ],
  "comment": "30 pages",
  "journal": "Journal of Differential Equations 253 (2012) pp. 41-72",
  "doi": "10.1016/j.jde.2012.03.022",
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain sharp $L^p$ and H\\\"older estimates for the Neumann function of the operator $\\nabla \\cdot \\gamma \\nabla - ik$ on a bounded domain. We also obtain quantitative description of its singularity. We then apply these estimates to quantitative photo-acoustic imaging in inhomogeneous media. The problem is to reconstruct the optical absorption coefficient of a diametrically small anomaly from the absorbed energy density.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-12T04:57:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B20",
      "35J25",
      "35J08"
    ],
    "keywords": [
      "quantitative photo-acoustic imaging",
      "neumann function",
      "inhomogeneous media",
      "sharp estimates",
      "applications"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Differential Equations",
      "year": 2012,
      "volume": 253,
      "number": 1,
      "pages": 41
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JDE...253...41A"
    }
  }
}