{
  "id": "2003.03725",
  "version": "v1",
  "published": "2020-03-08T05:40:16.000Z",
  "updated": "2020-03-08T05:40:16.000Z",
  "title": "Existence and regularity estimates for quasilinear equations with measure data: the case $1<p\\leq \\frac{3n-2}{2n-1}$",
  "authors": [
    "Quoc-Hung Nguyen",
    "Nguyen Cong Phuc"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain existence and global regularity estimates for gradients of solutions to quasilinear elliptic equations with measure data whose prototypes are of the form $-{\\rm div} (|\\nabla u|^{p-2} \\nabla u)= \\delta\\, |\\nabla u|^q +\\mu$ in a bounded main $\\Om\\subset\\RR^n$ potentially with non-smooth boundary. Here either $\\delta=0$ or $\\delta=1$, $\\mu$ is a finite signed Radon measure in $\\Omega$, and $q$ is of linear or super-linear growth, i.e., $q\\geq 1$. Our main concern is to extend earlier results to the strongly singular case $1<p\\leq \\frac{3n-2}{2n-1}$. In particular, in the case $\\delta=1$ which corresponds to a Riccati type equation, we settle the question of solvability that has been raised for some time in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-08T05:40:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J61",
      "35J62"
    ],
    "keywords": [
      "measure data",
      "quasilinear equations",
      "global regularity estimates",
      "finite signed radon measure",
      "quasilinear elliptic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}