{
  "id": "2410.09478",
  "version": "v1",
  "published": "2024-10-12T10:36:39.000Z",
  "updated": "2024-10-12T10:36:39.000Z",
  "title": "On the classification of extremals of Caffarelli-Kohn-Nirenberg inequalities",
  "authors": [
    "Giulio Ciraolo",
    "Camilla Chiara Polvara"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a family of critical elliptic equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities, possibly in convex cones in $\\mathbb{R}^d$, with $d\\geq 2$. We classify positive solutions without assuming that the solution has finite energy and when the intrinsic dimension $n \\in (\\frac{3}{2},5]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-12T10:36:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "caffarelli-kohn-nirenberg inequalities",
      "classification",
      "intrinsic dimension",
      "critical elliptic equations",
      "finite energy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}