{
  "abstract": "We establish universal interior Hölder and fractional energy estimates for stable solutions of $(-Δ)^su=f(u)$, $0<s<1$, with $f\\in C^1_{\\mathrm{loc}}(\\mathbb{R})$ nonnegative and convex. The bounds depend only on a weighted $L^1$ norm of the solution and hold under optimal conditions on the dimension and the fractional order. In particular, the half-Laplacian estimate holds through dimension eight. The estimates extend to stable finite-energy Dirichlet $L^1$-weak solutions without an a priori local boundedness assumption, and an explicit logarithmic solution proves optimality in this class. Applications include global bounds in convex domains, bounded extremal solutions, and a Liouville theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24727",
  "author_total": 1,
  "authors": [
    {
      "name": "Yiyang Xiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/50cgvg60wfxjd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24727",
  "fulltext_url": null,
  "id": "50cgvg60wfxjd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24727",
  "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": "W7223028839",
  "pdf_url": "https://arxiv.org/pdf/2610.24727",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/50cgvg60wfxjd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24727",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24727"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Universal Hölder estimates for stable solutions to semilinear equations of fractional order",
  "title_text": "Universal Hölder estimates for stable solutions to semilinear equations of fractional order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/50cgvg60wfxjd",
  "venue": "arXiv",
  "versions": []
}