{
  "id": "1911.08622",
  "version": "v1",
  "published": "2019-11-19T22:53:23.000Z",
  "updated": "2019-11-19T22:53:23.000Z",
  "title": "Regularity of solutions of quasi-linear elliptic equations with $L\\log^m L$ coefficients",
  "authors": [
    "Julian Edward",
    "Steve Hudson",
    "Mark Leckband"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $D$ be an bounded region in ${\\bf R}^n$. The regularity of solutions of a family of quasilinear elliptic partial differential equations is studied, one example being $\\Delta_nu=Vu^{n-1}$. The coefficients are assumed to be in the space $L\\log^{m}L(D)$ for $m>n-1$. Using a Moser iteration argument coupled with the Moser-Trudinger inequality, a local $L^{\\infty}$ bound on the solution $u$ is proven. A Harnack-type inequality is then proven. These results are shown to be sharp with respect to $m$. Then essential continuity of $u$ is proven, and away from the boundary a bound on the modulus of continuity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-19T22:53:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J62"
    ],
    "keywords": [
      "quasi-linear elliptic equations",
      "quasilinear elliptic partial differential equations",
      "coefficients",
      "regularity",
      "moser iteration argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}