{
  "abstract": "We study boundary regularity for the fully nonlinear singular elliptic equation of the form $|Du|^γF(D^2u)=f$, where $-1<γ<0$. First, we prove pointwise boundary $C^{1,α}$ estimates with pointwise $C^{1,α}$ Dirichlet data, which weakens the $C^2$ domain smoothness requirement from Birindelli and Demengel~\\cite{BD10}. The proof uses compactness and perturbation, without flattening the boundary. Second, we extend the $W^{2,δ}$ estimates of Li and Li~\\cite{LiLi17} from balls to $C^{1,α}$ domains with $C^{1,α}$ Dirichlet data{, for $0<δ\\leδ_0<1$. Here $δ_0$ is an exponent in the interior $W^{2,δ_0}$ estimate}. The proof combines pointwise boundary $C^{1,α}$ estimates, interior $W^{2,δ_0}$ estimates, and a Whitney decomposition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34238",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiqi Dong"
    },
    {
      "name": "Xuemei Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6h66y3e281yev.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34238",
  "fulltext_url": null,
  "id": "6h66y3e281yev",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34238",
  "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": "W7214802134",
  "pdf_url": "https://arxiv.org/pdf/2609.34238",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6h66y3e281yev.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34238",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34238"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Boundary Regularity for Fully Nonlinear Singular Elliptic Equations",
  "title_text": "Boundary Regularity for Fully Nonlinear Singular Elliptic Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/6h66y3e281yev",
  "venue": "arXiv",
  "versions": []
}