{
  "id": "1405.2999",
  "version": "v1",
  "published": "2014-05-12T23:42:49.000Z",
  "updated": "2014-05-12T23:42:49.000Z",
  "title": "The higher order regularity Dirichlet problem for elliptic systems in the upper-half space",
  "authors": [
    "José María Martell",
    "Dorina Mitrea",
    "Irina Mitrea",
    "Marius Mitrea"
  ],
  "journal": "Harmonic Analysis and Partial Differential Equations. Proceedings of the 9th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, June 11-15, 2012, Contemporary Mathematics 612 (2014), 123-141",
  "doi": "10.1090/conm/612/12228",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We identify a large class of constant (complex) coefficient, second order elliptic systems for which the Dirichlet problem in the upper-half space with data in $L^p$-based Sobolev spaces, $1<p<\\infty$, of arbitrary smoothness $\\ell$, is well-posed in the class of functions whose nontangential maximal operator of their derivatives up to, and including, order $\\ell$ is $L^p$-integrable. This class includes all scalar, complex coefficient elliptic operators of second order, as well as the Lam\\'e system of elasticity, among others.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-12T23:42:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J45",
      "35J57",
      "35C15",
      "74B05",
      "74G05"
    ],
    "keywords": [
      "higher order regularity dirichlet problem",
      "upper-half space",
      "complex coefficient elliptic operators",
      "second order elliptic systems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2999M"
    }
  }
}