{
  "id": "0903.0381",
  "version": "v1",
  "published": "2009-03-02T21:13:36.000Z",
  "updated": "2009-03-02T21:13:36.000Z",
  "title": "Profile of bubbling solutions to a Liouville system",
  "authors": [
    "Chang-shou Lin",
    "Lei Zhang"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "In several fields of Physics, Chemistry and Ecology, some models are described by Liouville systems. In this article we first prove a uniqueness result for a Liouville system in $\\mathbb R^2$. Then we establish an uniform estimate for bubbling solutions of a locally defined Liouville system near an isolated blowup point. The uniqueness result, as well as the local uniform estimates are crucial ingredients for obtaining a priori estimate, degree counting formulas and existence results for Liouville systems defined on Riemann surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-02T21:13:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J55"
    ],
    "keywords": [
      "bubbling solutions",
      "uniqueness result",
      "local uniform estimates",
      "riemann surfaces",
      "existence results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010AnIHP..27..117L"
    }
  }
}