{
  "id": "1709.05537",
  "version": "v1",
  "published": "2017-09-16T16:16:15.000Z",
  "updated": "2017-09-16T16:16:15.000Z",
  "title": "A priori estimates for some elliptic equations involving the $p$-Laplacian",
  "authors": [
    "Lucio Damascelli",
    "Rosa Pardo"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Dirichlet problem for positive solutions of the equation $-\\Delta_p (u) = f(u)$ in a convex, bounded, smooth domain $\\Omega \\subset\\R^N$, with $f$ locally Lipschitz continuous. \\par We provide sufficient conditions guarantying $L^{\\infty} $ a priori bounds for positive solutions of some elliptic equations involving the $p$-Laplacian and extend the class of known nonlinearities for which the solutions are $L^{\\infty} $ a priori bounded. As a consequence we prove the existence of positive solutions in convex bounded domains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-16T16:16:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B45",
      "35J92",
      "35B09",
      "35B33",
      "35J62"
    ],
    "keywords": [
      "elliptic equations",
      "priori estimates",
      "positive solutions",
      "convex bounded domains",
      "dirichlet problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}