{
  "id": "0904.3904",
  "version": "v2",
  "published": "2009-04-24T16:32:02.000Z",
  "updated": "2009-04-30T21:30:17.000Z",
  "title": "The $L^p$ Dirichlet Problem for the Stokes System on Lipschitz Domains",
  "authors": [
    "Joel Kilty"
  ],
  "comment": "To appear in Indiana Univ. Math. Journal. Updated to fix formatting issues",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the $L^p$ Dirichlet problem for the Stokes system on Lipschitz domains. For any fixed $p>2$, we show that a reverse H\\\"{o}lder condition with exponent $p$ is sufficient for the solvability of the Dirichlet problem with boundary data in $L^p_N(\\partial\\Omega,\\rn{d})$. Then we obtain a much simpler condition which implies the reverse H\\\"{o}lder condition. Finally, we establish the solvability ofthe $L^p$ Dirichlet problem for $d\\geq 4$ and $2-\\varepsilon<p<\\frac{2(d-1)}{d-3}+\\varepsilon$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-30T21:30:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30"
    ],
    "keywords": [
      "dirichlet problem",
      "stokes system",
      "lipschitz domains",
      "boundary data",
      "solvability ofthe"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.3904K"
    }
  }
}