{
  "id": "2312.16411",
  "version": "v1",
  "published": "2023-12-27T04:54:10.000Z",
  "updated": "2023-12-27T04:54:10.000Z",
  "title": "Wolff potential estimates and Wiener criterion for nonlocal equations with nonstandard growth",
  "authors": [
    "Minhyun Kim",
    "Ki-Ahm Lee",
    "Se-Chan Lee"
  ],
  "comment": "38 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the Wolff potential estimates for nonlocal equations with nonstandard growth. As an application, we obtain the Wiener criterion in this framework, which provides a necessary and sufficient condition for boundary points to be regular. Our approach relies on the fine analysis of superharmonic functions in view of nonlocal nonlinear potential theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-27T04:54:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C45",
      "31B25",
      "31B15",
      "35R11"
    ],
    "keywords": [
      "wolff potential estimates",
      "wiener criterion",
      "nonlocal equations",
      "nonstandard growth",
      "nonlocal nonlinear potential theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}