{
  "id": "1110.5189",
  "version": "v1",
  "published": "2011-10-24T10:34:58.000Z",
  "updated": "2011-10-24T10:34:58.000Z",
  "title": "The regularity problem for elliptic operators with boundary data in Hardy-Sobolev space $HS^1$",
  "authors": [
    "Martin Dindoš",
    "Josef Kirsch"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega$ be a Lipschitz domain in $\\mathbb R^n,n\\geq 3,$ and $L=\\divt A\\nabla$ be a second order elliptic operator in divergence form. We will establish that the solvability of the Dirichlet regularity problem for boundary data in Hardy-Sobolev space $\\HS$ is equivalent to the solvability of the Dirichlet regularity problem for boundary data in $H^{1,p}$ for some $1<p<\\infty$. This is a \"dual result\" to a theorem in \\cite{DKP09}, where it has been shown that the solvability of the Dirichlet problem with boundary data in $\\text{BMO}$ is equivalent to the solvability for boundary data in $L^p(\\partial\\Omega)$ for some $1<p<\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-24T10:34:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25"
    ],
    "keywords": [
      "boundary data",
      "hardy-sobolev space",
      "dirichlet regularity problem",
      "second order elliptic operator",
      "solvability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.5189D"
    }
  }
}