{
  "id": "1311.4783",
  "version": "v1",
  "published": "2013-11-19T15:40:55.000Z",
  "updated": "2013-11-19T15:40:55.000Z",
  "title": "The method of layer potentials in $L^p$ and endpoint spaces for elliptic operators with $L^\\infty$ coefficients",
  "authors": [
    "Steve Hofmann",
    "Marius Mitrea",
    "Andrew J. Morris"
  ],
  "comment": "37 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider layer potentials associated to elliptic operators $Lu=-{\\rm div}(A \\nabla u)$ acting in the upper half-space $\\mathbb{R}^{n+1}_+$ for $n\\geq 2$, or more generally, in a Lipschitz graph domain, where the coefficient matrix $A$ is $L^\\infty$ and $t$-independent, and solutions of $Lu=0$ satisfy interior estimates of De Giorgi/Nash/Moser type. A \"Calder\\'on-Zygmund\" theory is developed for the boundedness of layer potentials, whereby sharp $L^p$ and endpoint space bounds are deduced from $L^2$ bounds. Appropriate versions of the classical \"jump-relation\" formulae are also derived. The method of layer potentials is then used to establish well-posedness of boundary value problems for $L$ with data in $L^p$ and endpoint spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-19T15:40:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "58J32",
      "31B10",
      "31B15",
      "31A10",
      "45B05",
      "47G10",
      "78A30"
    ],
    "keywords": [
      "layer potentials",
      "elliptic operators",
      "endpoint space bounds",
      "lipschitz graph domain",
      "satisfy interior estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.4783H"
    }
  }
}