{
  "id": "0805.2533",
  "version": "v1",
  "published": "2008-05-16T13:50:33.000Z",
  "updated": "2008-05-16T13:50:33.000Z",
  "title": "Asymptotic behaviour for the gradient of large solutions to some nonlinear elliptic equations",
  "authors": [
    "Alessio Porretta",
    "Laurent Veron"
  ],
  "journal": "Advanced Nolinear Studies 6 (2006) 351-378",
  "categories": [
    "math.AP"
  ],
  "abstract": "If $h$ is a nondecreasing real valued function and $0\\leq q\\leq 2$, we analyse the boundary behaviour of the gradient of any solution $u$ of $-\\Delta u+h(u)+\\abs {\\nabla u}^q=f$ in a smooth N-dimensional domain $\\Omega$ with the condition that $u$ tends to infinity when $x$ tends to $\\partial\\Omega$. We give precise expressions of the blow-up which, in particular, point out the fact that the phenomenon occurs essentially in the normal direction to $\\partial\\Omega$. Motivated by the blow--up argument in our proof, we also give in Appendix a symmetry result for some related problems in the half space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-16T13:50:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60"
    ],
    "keywords": [
      "nonlinear elliptic equations",
      "asymptotic behaviour",
      "large solutions",
      "smooth n-dimensional domain",
      "nondecreasing real valued function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.2533P"
    }
  }
}