{
  "id": "1405.4410",
  "version": "v1",
  "published": "2014-05-17T15:25:02.000Z",
  "updated": "2014-05-17T15:25:02.000Z",
  "title": "On properties of solutions of quasilinear second-order elliptic inequalities",
  "authors": [
    "Andrej A. Kon'kov"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega$ be an unbounded open subset of ${\\mathbb R}^n$, $n \\ge 2$, and $A : \\Omega \\times {\\mathbb R}^n \\to {\\mathbb R}^n$ be a function such that $$ C_1 |\\zeta|^p \\le \\zeta A (x, \\zeta), \\quad |A (x, \\zeta)| \\le C_2 |\\zeta|^{p-1} $$ with some constants $C_1 > 0$, $C_2 > 0$, and $p > 1$ for almost all $x \\in \\Omega$ and for all $\\zeta \\in {\\mathbb R}^n$. We obtain blow-up conditions and priori estimates for inequalities of the form $$ {\\rm div} \\, A (x, D u) + b (x) |D u|^\\alpha \\ge q (x) g (u) \\quad \\mbox{in } \\Omega, $$ where $p - 1 \\le \\alpha \\le p$ is a real number and, moreover, $b \\in L_{\\infty, loc} (\\Omega)$, $q \\in L_{\\infty, loc} (\\Omega)$, and $g \\in C ([0, \\infty))$ are non-negative functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-17T15:25:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "35J60",
      "35J61",
      "35J62",
      "35J92"
    ],
    "keywords": [
      "quasilinear second-order elliptic inequalities",
      "properties",
      "real number",
      "unbounded open subset",
      "priori estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.4410K"
    }
  }
}