{
  "id": "1902.04806",
  "version": "v1",
  "published": "2019-02-13T09:34:02.000Z",
  "updated": "2019-02-13T09:34:02.000Z",
  "title": "Weak solutions of semilinear elliptic equations with Leray-Hardy potential and measure data",
  "authors": [
    "Laurent Veron",
    "Huyuan Chen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study existence and stability of solutions of (E 1) --$\\Delta$u + $\\mu$ |x| 2 u + g(u) = $\\nu$ in $\\Omega$, u = 0 on $\\partial$$\\Omega$, where $\\Omega$ is a bounded, smooth domain of R N , N $\\ge$ 2, containing the origin, $\\mu$ $\\ge$ -- (N --2) 2 4 is a constant, g is a nondecreasing function satisfying some integral growth assumption and $\\nu$ is a Radon measure on $\\Omega$. We show that the situation differs according $\\nu$ is diffuse or concentrated at the origin. When g is a power we introduce a capacity framework to find necessary and sufficient condition for solvability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-13T09:34:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semilinear elliptic equations",
      "leray-hardy potential",
      "measure data",
      "weak solutions",
      "study existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}