{
  "id": "1802.03432",
  "version": "v1",
  "published": "2018-02-09T19:55:15.000Z",
  "updated": "2018-02-09T19:55:15.000Z",
  "title": "Asymptotic analysis and energy quantization for the Lane-Emden problem in dimension two",
  "authors": [
    "Francesca De Marchis",
    "Massimo Grossi",
    "Isabella Ianni",
    "Filomena Pacella"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We complete the study of the asymptotic behavior, as $p\\rightarrow +\\infty$, of the positive solutions to \\[ \\left\\{\\begin{array}{lr}-\\Delta u= u^p & \\mbox{in}\\Omega\\\\ u=0 &\\mbox{on}\\partial \\Omega \\end{array}\\right. \\] when $\\Omega$ is any smooth bounded domain in $\\mathbb R^2$, started in [4]. In particular we show quantization of the energy to multiples of $8\\pi e$ and prove convergence to $\\sqrt{e}$ of the $L^{\\infty}$-norm, thus confirming the conjecture made in [4].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-09T19:55:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "energy quantization",
      "lane-emden problem",
      "asymptotic analysis",
      "smooth bounded domain",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}