{
  "abstract": "We prove boundary Hölder regularity for fractional porous medium-type equations in bounded smooth domains with zero exterior data. For $0<σ<1$, $n>2σ$, and $m>1$, we show that nonnegative weak dual solutions $v$ of $\\partial_t v+(-Δ)^σ(v^m)=0$ satisfy \\[ \\frac{v}{d^{σ/m}}\\in C_{x,t}^{α,\\frac{αm}{σ(m+1)}} \\] up to the boundary and away from the initial time, for some $α\\in(0,σ)$, where $d$ denotes the distance to the boundary. More generally, we establish boundary Hölder estimates for $u/d^σ$ for nonnegative viscosity solutions of $\\partial_t u=u^γLu$, with $0<γ<1$ and initial data comparable to $d^σ$. Here $L$ is a symmetric stable operator of order $2σ$ whose measurable angular density is bounded above and below by positive constants. Our proof combines comparison principles and boundary barriers with a blow-up and compactness argument based on a Liouville theorem for ancient solutions in a half-space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16113",
  "author_total": 3,
  "authors": [
    {
      "name": "Mengyu Huo"
    },
    {
      "name": "Tianling Jin"
    },
    {
      "name": "Jingang Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ndr9ag9193dg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16113",
  "fulltext_url": null,
  "id": "2ndr9ag9193dg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16113",
  "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": "W7221768099",
  "pdf_url": "https://arxiv.org/pdf/2610.16113",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ndr9ag9193dg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16113",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16113"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Boundary regularity for fractional porous medium-type equations in bounded domains",
  "title_text": "Boundary regularity for fractional porous medium-type equations in bounded domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/2ndr9ag9193dg",
  "venue": "arXiv",
  "versions": []
}