{
  "abstract": "We prove smoothness up to the boundary for $k$-Hessian eigenfunctions on smooth bounded uniformly convex domains when $2\\leq k<n$. This resolves an open problem in the regularity theory of degenerate fully nonlinear elliptic equations and extends the boundary smoothness theorem for Monge--Ampère eigenfunctions. In contrast to the Monge--Ampère case, the linearized $k$-Hessian operator remains uniformly elliptic up to the boundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31445",
  "author_total": 2,
  "authors": [
    {
      "name": "Guohuan Qiu"
    },
    {
      "name": "Jin Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ch7x69kx8fp75.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31445",
  "fulltext_url": null,
  "id": "ch7x69kx8fp75",
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  "landing_url": "https://arxiv.org/abs/2610.31445",
  "language": null,
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  "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": "W7223263661",
  "pdf_url": "https://arxiv.org/pdf/2610.31445",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ch7x69kx8fp75.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31445",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31445"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Boundary regularity of $k$-Hessian eigenfunctions",
  "title_text": "Boundary regularity of k-Hessian eigenfunctions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/ch7x69kx8fp75",
  "venue": "arXiv",
  "versions": []
}