{
  "id": "1411.4719",
  "version": "v1",
  "published": "2014-11-18T02:29:12.000Z",
  "updated": "2014-11-18T02:29:12.000Z",
  "title": "Boundary integral operator for the fractional Laplacian in the bounded smooth domain",
  "authors": [
    "TongKeun Chang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the boundary integral operator induced from the fractional Laplace equation in a bounded smooth domain. For $1/2 < \\alpha? < 1$, we show the bijectivity of the boundary integral operator $S_{2\\alpha} : L^p(\\partial \\Omega) \\rightarrow H^{2\\alpha-1}_p (\\partial \\Omega), 1 < p < 1$. As an application, we show the existence of the solution of the boundary value problem of the fractional Laplace equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-18T02:29:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded smooth domain",
      "fractional laplacian",
      "fractional laplace equation",
      "boundary value problem",
      "boundary integral operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.4719C"
    }
  }
}