{
  "abstract": "We investigate interior regularity for stable solutions of the semilinear elliptic equation $-Δu=f(u)$ in an open set $Ω\\subseteq \\mathbb R^n$, where $f$ is locally Lipschitz and may change sign. We establish sharp interior Hölder estimates for stable classical solutions in every dimension $n\\le 9$, thereby fully resolving a question raised by Cabré concerning interior regularity without the nonnegativity assumption on $f$. For $n\\le 5$, we also give a short alternative proof of the corresponding Hölder regularity result due to Peng, Zhang, and Zhou. We further establish higher-integrability estimates for the gradient and $L^1$ bounds for the Hessian in all dimensions. For $n\\ge 10$, we obtain BMO and Morrey estimates, extending related results previously established for nonnegative nonlinearities. When $f$ is convex, we extend the interior regularity estimates to stable weak solutions through an approximation theorem. As applications, we prove Liouville-type theorems for entire stable solutions of equations with sign-changing nonlinearities across all dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21641",
  "author_total": 3,
  "authors": [
    {
      "name": "Long-Han Huang"
    },
    {
      "name": "Yuxuan Zhou"
    },
    {
      "name": "Wenming Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/36mjjckhgket7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21641",
  "fulltext_url": null,
  "id": "36mjjckhgket7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21641",
  "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": "W7222692447",
  "pdf_url": "https://arxiv.org/pdf/2610.21641",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/36mjjckhgket7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21641",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21641"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Interior Regularity for Stable Solutions of Semilinear Elliptic Equations with Sign-Changing Nonlinearities",
  "title_text": "Interior Regularity for Stable Solutions of Semilinear Elliptic Equations with Sign-Changing Nonlinearities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/36mjjckhgket7",
  "venue": "arXiv",
  "versions": []
}