{
  "id": "2108.03878",
  "version": "v1",
  "published": "2021-08-09T08:55:52.000Z",
  "updated": "2021-08-09T08:55:52.000Z",
  "title": "On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part III",
  "authors": [
    "Naian Liao",
    "Leah Schätzler"
  ],
  "comment": "This work continues arXiv:2003.04158 and arXiv:2108.02749",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the local H\\\"older continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \\[ \\partial_t\\big(|u|^{q-1}u\\big)-\\Delta_p u=0,\\quad 1<p<2,\\quad 0<p-1<q. \\] The proof exploits the space expansion of positivity for the singular, parabolic $p$-Laplacian and employs the method of intrinsic scaling by carefully balancing the double singularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-09T08:55:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "doubly nonlinear equation",
      "hölder regularity",
      "signed solutions",
      "doubly nonlinear parabolic equations",
      "space expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}