{
  "id": "2202.04571",
  "version": "v1",
  "published": "2022-02-09T17:08:50.000Z",
  "updated": "2022-02-09T17:08:50.000Z",
  "title": "Harnack inequality for nonlocal problems with non-standard growth",
  "authors": [
    "Jamil Chaker",
    "Minhyun Kim",
    "Marvin Weidner"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a full Harnack inequality for local minimizers, as well as weak solutions to nonlocal problems with non-standard growth. The main auxiliary results are local boundedness and a weak Harnack inequality for functions in a corresponding De Giorgi class. This paper builds upon a recent work on regularity estimates for such nonlocal problems by the same authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-09T17:08:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "47G20",
      "35D30",
      "35B45",
      "35A15"
    ],
    "keywords": [
      "nonlocal problems",
      "non-standard growth",
      "weak harnack inequality",
      "main auxiliary results",
      "full harnack inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}