{
  "id": "2111.03875",
  "version": "v1",
  "published": "2021-11-06T12:57:48.000Z",
  "updated": "2021-11-06T12:57:48.000Z",
  "title": "A stability result for elliptic equations with singular nonlinearity and its applications to homogenization problems",
  "authors": [
    "Takanobu Hara"
  ],
  "journal": "J. Math. Anal. Appl. 528, 1 (2023)",
  "doi": "10.1016/j.jmaa.2023.127509",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider model semilinear elliptic equations of the type \\[ \\begin{cases} - \\mathrm{div} (A(x) \\nabla u) = f u^{- \\lambda}, \\quad u > 0 \\quad \\text{in} \\ \\Omega, \\\\ u \\in H_{0}^{1}(\\Omega), \\end{cases} \\] where $\\Omega$ is a bounded domain in $\\mathbf{R}^{N}$, $N \\ge 1$, $A \\in L^{\\infty}(\\Omega)^{N \\times N}$ is a coercive matrix, $0 < \\lambda \\le 1$ and $f$ is a nonnegative function in $L^{1}_{loc}(\\Omega)$, or more generally, nonnegative Radon measure on $\\Omega$. We discuss $H^{1}$-stability of $u$ under a minimal assumption on $f$. Additionally, we apply the result to homogenization problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-11-06T12:57:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35J25",
      "35B27"
    ],
    "keywords": [
      "homogenization problems",
      "stability result",
      "singular nonlinearity",
      "applications",
      "model semilinear elliptic equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}