{
  "id": "1509.03897",
  "version": "v1",
  "published": "2015-09-13T20:40:08.000Z",
  "updated": "2015-09-13T20:40:08.000Z",
  "title": "Monotonicity in half-spaces of positive solutions to $-Δ_p u=f(u)$ in the case $p>2$",
  "authors": [
    "Alberto Farina",
    "Luigi Montoro",
    "Berardino Sciunzi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider weak distributional solutions to the equation $-\\Delta_pu=f(u)$ in half-spaces under zero Dirichlet boundary condition. We assume that the nonlinearity is positive and superlinear at zero. For $p>2$ (the case $1<p\\leq2$ is already known) we prove that any positive solution is strictly monotone increasing in the direction orthogonal to the boundary of the half-space. As a consequence we deduce some Liouville type theorems for the Lane-Emden type equation. Furthermore any nonnegative solution turns out to be $C^{2,\\alpha}$ smooth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-13T20:40:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive solution",
      "half-space",
      "monotonicity",
      "zero dirichlet boundary condition",
      "lane-emden type equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}