{
  "abstract": "With the aim of extending to parabolic equations the framework developed by the first three authors in [Dipierro, Savin, and Valdinoci, Rev. Mat. Iberoam. (2019)], we introduce a notion of (viscosity) solutions for the space-fractional heat equation modulo $k$. In turn, we are able to define $s$-caloric functions with polynomial growth at infinity, showing also related Schauder estimates, a Liouville-type result, and a stability property with respect to the $L^\\infty_{\\rm{loc}}$-convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03840",
  "author_total": 4,
  "authors": [
    {
      "name": "Serena Dipierro"
    },
    {
      "name": "Ovidiu Savin"
    },
    {
      "name": "Enrico Valdinoci"
    },
    {
      "name": "Riccardo Villa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/axfnnws08a5h3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03840",
  "fulltext_url": null,
  "id": "axfnnws08a5h3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03840",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/axfnnws08a5h3.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Solutions of the space-fractional heat equation with polynomial growth: Liouville theorems and Schauder estimates",
  "title_text": "Solutions of the space-fractional heat equation with polynomial growth: Liouville theorems and Schauder estimates",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/axfnnws08a5h3",
  "venue": "arXiv",
  "versions": []
}