{
  "id": "math/0411120",
  "version": "v1",
  "published": "2004-11-05T16:57:38.000Z",
  "updated": "2004-11-05T16:57:38.000Z",
  "title": "The $L^p$ Dirichlet Problem for Elliptic Systems on Lipschitz Domains",
  "authors": [
    "Zhongwei Shen"
  ],
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We develop a new approach to the $L^p$ Dirichlet problem via $L^2$ estimates and reverse Holder inequalities. We apply this approach to second order elliptic systems and the polyharmonic equation on a bounded Lipschitz domain $\\Omega$ in $R^n$. For $n\\ge 4$ and $2-\\epsilon<p<2(n-1)/(n-3)+\\epsilon$, we establish the solvability of the Dirichlet problem with boundary value data in $L^p(\\partial\\Omega)$. In the case of the polyharmonic equation $\\Delta^{\\ell}u=0$ with $\\ell\\ge 2$, the range of $p$ is sharp if $4\\le n \\le 2\\ell +1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-05T16:57:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J55",
      "35J40"
    ],
    "keywords": [
      "dirichlet problem",
      "second order elliptic systems",
      "polyharmonic equation",
      "reverse holder inequalities",
      "boundary value data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11120S"
    }
  }
}