{
  "id": "1312.6498",
  "version": "v1",
  "published": "2013-12-23T09:48:50.000Z",
  "updated": "2013-12-23T09:48:50.000Z",
  "title": "Kato's inequality when $Δu$ is a measure",
  "authors": [
    "Haïm Brezis",
    "Augusto C. Ponce"
  ],
  "journal": "C. R. Acad. Sci. Paris, Ser. I 338 (2004), 599--604",
  "categories": [
    "math.AP"
  ],
  "abstract": "We extend the classical Kato's inequality in order to allow functions $u \\in L^1_\\mathrm{loc}$ such that $\\Delta u$ is a Radon measure. This inequality has been applied by Brezis, Marcus, and Ponce to study the existence of solutions of the nonlinear equation $- \\Delta u + g(u) = \\mu$, where $\\mu$ is a measure and $g : \\mathbb{R} \\to \\mathbb{R}$ is an increasing continuous function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-23T09:48:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear equation",
      "classical katos inequality",
      "radon measure",
      "increasing continuous function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.6498B"
    }
  }
}