{
  "id": "2105.13612",
  "version": "v1",
  "published": "2021-05-28T06:45:03.000Z",
  "updated": "2021-05-28T06:45:03.000Z",
  "title": "The concentration-compactness principle for the nonlocal anisotropic $p$-Laplacian of mixed order",
  "authors": [
    "Jamil Chaker",
    "Minhyun Kim",
    "Marvin Weidner"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the existence of minimizers of the Sobolev quotient for a class of nonlocal operators with an orthotropic structure having different exponents of integrability and different orders of differentiability. Our method is based on the concentration-compactness principle which we extend to this class of operators. One consequence of our main result is the existence of a nontrivial nonnegative solution to the corresponding critical problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-28T06:45:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "35A01",
      "49J35",
      "46E35",
      "46B50"
    ],
    "keywords": [
      "concentration-compactness principle",
      "nonlocal anisotropic",
      "mixed order",
      "sobolev quotient",
      "nonlocal operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}