{
  "id": "1807.04432",
  "version": "v1",
  "published": "2018-07-12T06:14:12.000Z",
  "updated": "2018-07-12T06:14:12.000Z",
  "title": "Existence of bubbling solutions without mass concentration",
  "authors": [
    "Youngae Lee",
    "Chang-Shou Lin",
    "Wen Yang"
  ],
  "comment": "This paper will appear at Annales de l'Institut Fourier",
  "categories": [
    "math.AP"
  ],
  "abstract": "The seminal work \\cite{bm} by Brezis and Merle has been pioneering in studying the bubbling phenomena of the mean field equation with singular sources. When the vortex points are not collapsing, the mean field equation possesses the property of the so-called \"bubbling implies mass concentration\". Recently, Lin and Tarantello in \\cite{lt} pointed out that the \"bubbling implies mass concentration\" phenomena might not hold in general if the collapse of singularities occurs. In this paper, we shall construct the first concrete example of non-concentrated bubbling solution of the mean field equation with collapsing singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-12T06:14:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bubbling solution",
      "bubbling implies mass concentration",
      "mean field equation possesses",
      "first concrete example",
      "singular sources"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}