{
  "id": "1211.6542",
  "version": "v2",
  "published": "2012-11-28T08:31:24.000Z",
  "updated": "2013-02-13T15:25:42.000Z",
  "title": "Remarks on some quasilinear equations with gradient terms and measure data",
  "authors": [
    "Marie-Françoise Bidaut-Véron",
    "Marta Garcia-Huidobro",
    "Laurent Veron"
  ],
  "comment": "To appear in Contemporary Mathematics",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega \\subset \\mathbb{R}^{N}$ be a smooth bounded domain, $H$ a Caratheodory function defined in $\\Omega \\times \\mathbb{R\\times R}^{N},$ and $\\mu $ a bounded Radon measure in $\\Omega .$ We study the problem% \\begin{equation*} -\\Delta_{p}u+H(x,u,\\nabla u)=\\mu \\quad \\text{in}\\Omega,\\qquad u=0\\quad \\text{on}\\partial \\Omega, \\end{equation*} where $\\Delta_{p}$ is the $p$-Laplacian ($p>1$)$,$ and we emphasize the case $H(x,u,\\nabla u)=\\pm \\left\\| \\nabla u\\right\\| ^{q}$ ($q>0$). We obtain an existence result under subcritical growth assumptions on $H,$ we give necessary conditions of existence in terms of capacity properties, and we prove removability results of eventual singularities. In the supercritical case, when $\\mu \\geqq 0$ and $H$ is an absorption term, i.e. $% H\\geqq 0,$ we give two sufficient conditions for existence of a nonnegative solution.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-13T15:25:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gradient terms",
      "quasilinear equations",
      "measure data",
      "existence result",
      "absorption term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.6542B"
    }
  }
}