{
  "id": "1402.0593",
  "version": "v1",
  "published": "2014-02-03T12:02:15.000Z",
  "updated": "2014-02-03T12:02:15.000Z",
  "title": "On the mass of the exterior blow-up points",
  "authors": [
    "Samy Skander Bahoura"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1309.1582, arXiv:1302.0657",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the following problem on open set $\\Omega$ of ${\\mathbb R}^2$: $$\\left \\{ \\begin {split} -\\Delta u_i & = V_i e^{u_i} \\,\\, &\\text{in} \\,\\, &\\Omega \\subset {\\mathbb R}^2, \\\\ u_i & = 0 \\,\\, & \\text{in} \\,\\, &\\partial \\Omega.\\end {split}\\right.$$ We assume that $ \\int_{\\Omega} e^{u_i} dy \\leq C$, and $ 0 \\leq V_i \\leq b < + \\infty$. On the other hand, if we assume that $V_i$ $s-$holderian with $1/2< s \\leq 1$, then each exterior blow-up point is simple. As application, we have a compactness result for the case when: $\\int_{\\Omega}V_i e^{u_i} dy \\leq 40\\pi-\\epsilon , \\,\\, \\epsilon >0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-03T12:02:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exterior blow-up point",
      "open set",
      "compactness result",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.0593S"
    }
  }
}