{
  "id": "2008.03597",
  "version": "v1",
  "published": "2020-08-08T20:56:43.000Z",
  "updated": "2020-08-08T20:56:43.000Z",
  "title": "Regularizing effect of absorption terms in singular and degenerate elliptic problems",
  "authors": [
    "Abdelaaziz Sbai",
    "Youssef El Hadfi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the existence and regularity of solutions to the following singular problem \\begin{equation} \\left\\{ \\begin{array}{lll} &-\\displaystyle\\mbox{div} \\big(a(x,u)|\\nabla u|^{p-2}|\\nabla u|\\big) + |u|^{s-1}u =\\frac{f}{u^{\\gamma}} &\\mbox{ in } \\Omega \\\\ &u>0 &\\mbox{ in }\\Omega \\\\ &u=0 &\\mbox{ on } \\delta\\Omega \\end{array} \\right. \\end{equation} proving that the lower order term $u|u|^{s-1}$ has some regularizing effects on the solutions in the case of an elliptic operator with degenerate coercivity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-08T20:56:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A21",
      "35B20",
      "35B25",
      "35B45",
      "35D30",
      "35J60",
      "35J70",
      "35J75"
    ],
    "keywords": [
      "degenerate elliptic problems",
      "regularizing effect",
      "absorption terms",
      "lower order term",
      "singular problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}