{
  "id": "1910.07101",
  "version": "v1",
  "published": "2019-10-15T23:18:18.000Z",
  "updated": "2019-10-15T23:18:18.000Z",
  "title": "Phase separation, optimal partitions, and nodal solutions to the Yamabe equation on the sphere",
  "authors": [
    "Mónica Clapp",
    "Alberto Saldaña",
    "Andrzej Szulkin"
  ],
  "comment": "16 pages and 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study an optimal M-partition problem for the Yamabe equation on the round sphere, in the presence of some particular symmetries. We show that there is a correspondence between solutions to this problem and least-energy sign-changing symmetric solutions to the Yamabe equation on the sphere with precisely M nodal domains. The existence of an optimal partition is established through the study of the limit profiles of least-energy solutions to a weakly coupled competitive elliptic system on the sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-15T23:18:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05",
      "58J32",
      "35J50",
      "35B06",
      "35B08",
      "35B33"
    ],
    "keywords": [
      "yamabe equation",
      "optimal partition",
      "phase separation",
      "nodal solutions",
      "coupled competitive elliptic system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}