{
  "id": "2401.12057",
  "version": "v1",
  "published": "2024-01-22T15:50:02.000Z",
  "updated": "2024-01-22T15:50:02.000Z",
  "title": "Asymptotic Analysis and Uniqueness of blowup solutions of non-quantized singular mean field equations",
  "authors": [
    "Daniele Bartoclucci",
    "Wen Yang",
    "Lei Zhang"
  ],
  "comment": "76 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions as far as blowup points are either regular points or non-quantized singular sources. In particular the uniqueness result covers the most general case improving all previous works of Bartolucci-Jevnikar-Lee-Yang \\cite{bart-4,bart-4-2} and Wu-Zhang \\cite{wu-zhang-ccm}. For example, unlike previous results, we drop the assumption of singular sources being critical points of a suitably defined Kirchoff-Routh type functional. Based on refined estimates which allow a major simplification of previous proofs, our new argument is robust and flexible enough to be applied to a wide range of problems requiring a delicate blowup analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-22T15:50:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "53C21"
    ],
    "keywords": [
      "non-quantized singular mean field equations",
      "asymptotic analysis",
      "blowup solutions",
      "defined kirchoff-routh type functional",
      "uniqueness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 76,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}