{
  "id": "0810.5140",
  "version": "v1",
  "published": "2008-10-28T20:54:19.000Z",
  "updated": "2008-10-28T20:54:19.000Z",
  "title": "A priori estimate for a family of semi-linear elliptic equations with critical nonlinearity",
  "authors": [
    "Lei Zhang"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider positive solutions of $\\Delta u-\\mu u+Ku^{\\frac{n+2}{n-2}}=0$ on $B_1$ ($n\\ge 5$) where $\\mu $ and $K>0$ are smooth functions on $B_1$. If $K$ is very sub-harmonic at each critical point of $K$ in $B_{2/3}$ and the maximum of $u$ in $\\bar B_{1/3}$ is comparable to its maximum over $\\bar B_1$, then all positive solutions are uniformly bounded on $\\bar B_{1/3}$. As an application, a priori estimate for solutions of equations defined on $\\mathbb S^n$ is derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-28T20:54:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "53C21"
    ],
    "keywords": [
      "semi-linear elliptic equations",
      "priori estimate",
      "critical nonlinearity",
      "positive solutions",
      "smooth functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}