{
  "id": "2307.04426",
  "version": "v1",
  "published": "2023-07-10T09:02:44.000Z",
  "updated": "2023-07-10T09:02:44.000Z",
  "title": "The Brezis-Nirenberg problem in 4D",
  "authors": [
    "Angela Pistoia",
    "Serena Rocci"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The problem \\begin{equation} \\label{bn} -\\Delta u=|u|^{4\\over n-2}u+\\lambda V u\\ \\hbox{in}\\ \\Omega,\\ u=0\\ \\hbox{on}\\ \\partial\\Omega \\end{equation} where $\\Omega$ is a bounded regular domain in $\\mathbb R^n$, $\\lambda\\in \\mathbb R$ and $V\\in C^0(\\overline \\Omega),$ that was introduced by Brezis and Nirenberg in their famous paper, where they address the existence of positive solutions in the autonomous case, i.e. the potential $V$ is constant. Since then, a huge amount of work has been done. In the following we will make a brief history highlighting the results which are much closer to the problem we wish to study in the present paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-10T09:02:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brezis-nirenberg problem",
      "bounded regular domain",
      "brief history",
      "famous paper",
      "autonomous case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}