{
  "abstract": "We study non-negative weak solutions to a class of doubly nonlinear nonlocal parabolic equations of the form $$ (u^q)_t+\\mathcal Lu=0, $$ where $\\mathcal L$ is a nonlocal $p$-Laplace-type operator with a symmetric measurable kernel. We consider the fast-diffusion range $1<p<q+1$ and establish Harnack-type estimates in the upper fast-diffusion regime $\\widetilde p_c<p<q+1$, where $\\widetilde p_c$ is a critical exponent determined by the interplay between the temporal nonlinearity and the nonlocal diffusion. In particular, the estimates apply to the nonlocal parabolic $p$-Laplace equation and the nonlocal porous medium equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29553",
  "author_total": 3,
  "authors": [
    {
      "name": "Mariia Savchenko"
    },
    {
      "name": "Igor Skrypnik"
    },
    {
      "name": "Yevgeniia Yevgenieva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5aersvjdpbsf1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29553",
  "fulltext_url": null,
  "id": "5aersvjdpbsf1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29553",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223238270",
  "pdf_url": "https://arxiv.org/pdf/2610.29553",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5aersvjdpbsf1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29553",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29553"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Harnack-type inequalities for nonlocal parabolic equations in the upper fast-diffusion range",
  "title_text": "Harnack-type inequalities for nonlocal parabolic equations in the upper fast-diffusion range",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/5aersvjdpbsf1",
  "venue": "arXiv",
  "versions": []
}