{
  "abstract": "In this paper, we study Hölder regularity of local weak super-solutions to the parabolic equation associated with fractional $p$-Laplacian type operators $$ \\partial_t u(t,x)-\\text{p.v.}\\int_{\\R^d}|u(t,y)-u(t,x)|^{p-2}(u(t,y)-u(t,x))J(t;x,y)\\,dy=0,\\quad (t,x)\\in \\R\\times \\R^d, $$ where $\\text{p.v.}$ denotes the principal value, $p\\in(1,\\infty)$ and the kernel $J(t;x,y)$ is comparable (uniformly with respect to $(t;x,y)\\in\\R\\times\\R^d\\times\\R^d$) to the fractional $p$-Laplacian kernel $|x-y|^{-d-sp}$ with $s\\in(0,1)$. Our contribution extends the fundamental work of Kassmann and Weidner to the nonlinear case $p\\ne 2$. In particular, we provide an explicit nonlocal parabolic tail condition in terms of an $L^{1+\\varepsilon}$-norm in the time variable (for a suitable $\\varepsilon>0$) for all $p\\in(1,\\infty)$, under which Hölder regularity holds. Our proof is based on the method of expansion of positivity, which is the key ingredient in the reduction-of-oscillation argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13539",
  "author_total": 3,
  "authors": [
    {
      "name": "Takashi Kumagai"
    },
    {
      "name": "Jian Wang"
    },
    {
      "name": "Meng-ge Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/625xrb8gfgaj6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13539",
  "fulltext_url": null,
  "id": "625xrb8gfgaj6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13539",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221562820",
  "pdf_url": "https://arxiv.org/pdf/2610.13539",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/625xrb8gfgaj6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13539",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13539"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Hölder regularity of solutions to parabolic equations associated with fractional $p$-Laplacian type operators",
  "title_text": "Hölder regularity of solutions to parabolic equations associated with fractional p-Laplacian type operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/625xrb8gfgaj6",
  "venue": "arXiv",
  "versions": []
}