{
  "id": "0902.0449",
  "version": "v3",
  "published": "2009-02-03T08:56:26.000Z",
  "updated": "2009-07-14T21:02:35.000Z",
  "title": "Isolated Boundary Singularities of Semilinear Elliptic Equations",
  "authors": [
    "Marie-Françoise Bidaut-Veron",
    "Augusto C. Ponce",
    "Laurent Veron"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Given a smooth domain $\\Omega\\subset\\RR^N$ such that $0 \\in \\partial\\Omega$ and given a nonnegative smooth function $\\zeta$ on $\\partial\\Omega$, we study the behavior near 0 of positive solutions of $-\\Delta u=u^q$ in $\\Omega$ such that $u = \\zeta$ on $\\partial\\Omega\\setminus\\{0\\}$. We prove that if $\\frac{N+1}{N-1} < q < \\frac{N+2}{N-2}$, then $u(x)\\leq C \\abs{x}^{-\\frac{2}{q-1}}$ and we compute the limit of $\\abs{x}^{\\frac{2}{q-1}} u(x)$ as $x \\to 0$. We also investigate the case $q= \\frac{N+1}{N-1}$. The proofs rely on the existence and uniqueness of solutions of related equations on spherical domains.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-07-14T21:02:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "34B15"
    ],
    "keywords": [
      "semilinear elliptic equations",
      "isolated boundary singularities",
      "smooth domain",
      "nonnegative smooth function",
      "positive solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.0449B"
    }
  }
}