{
  "abstract": "This work aims to present a new proof of the global pointwise Harnack inequality satisfied by positive viscosity solutions of the doubly nonlinear heat equation on $\\mathbb{R}^d$. Our approach is based on a multi-point maximum principle argument introduced by the authors in a recent article [Calc. Var., 2026]. Required for the proof is a new variation of the maximum principle for semicontinuous functions, which is a standard tool in the analysis of viscosity solutions. In particular, our techniques provide a new proof of the Harnack inequalities satisfied by positive solutions of the porous medium equation and the $p$-heat equation, which were derived by Auchmuty and Bao [Proc. Amer. Math. Soc., 1994] using results of Aronson and Bénilan [C. R. Acad. Sci. Paris, 1979] and Esteban and Vázquez [Arch. Rational Mech. Anal., 1988]. The results contained in this article have also been discussed in the third author's doctoral thesis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21732",
  "author_total": 3,
  "authors": [
    {
      "name": "Ben Andrews"
    },
    {
      "name": "Daniel Hauer"
    },
    {
      "name": "Jessica Slegers"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1nzk12newt6cs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21732",
  "fulltext_url": null,
  "id": "1nzk12newt6cs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21732",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7222546628",
  "pdf_url": "https://arxiv.org/pdf/2610.21732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1nzk12newt6cs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21732"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A multi-point maximum principle to prove the global Harnack inequality for the doubly nonlinear heat equation",
  "title_text": "A multi-point maximum principle to prove the global Harnack inequality for the doubly nonlinear heat equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/1nzk12newt6cs",
  "venue": "arXiv",
  "versions": []
}