{
  "id": "2204.13196",
  "version": "v1",
  "published": "2022-04-27T21:12:44.000Z",
  "updated": "2022-04-27T21:12:44.000Z",
  "title": "Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations",
  "authors": [
    "Prashanta Garain",
    "Erik Lindgren"
  ],
  "comment": "38 pages, comments are welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider equations involving a combination of local and nonlocal degenerate $p$-Laplace operators. The main contribution of the paper is almost Lipschitz regularity for the homogeneous equation and H\\\"older continuity with an explicit H\\\"older exponent in the general case. For certain parameters, our results also imply H\\\"older continuity of the gradient. In addition, we establish existence, uniqueness and local boundedness. The approach is based on an iteration in the spirit of Moser combined with an approximation method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-27T21:12:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35D30",
      "35J70",
      "35R09",
      "35R11"
    ],
    "keywords": [
      "nonlocal degenerate elliptic equations",
      "higher hölder regularity",
      "mixed local",
      "main contribution",
      "lipschitz regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}