{
  "abstract": "We investigate the partial regularity of viscosity solutions to fully nonlinear elliptic equations of the form $F(D^2u, x) = f(x)$ in previously unexplored settings: (i) When $F$ is non-differentiable with respect to $D^2u$. (ii) When either $F$ or $f$ lacks Dini continuity in $x$. In the first scenario, we introduce a tangent operator property for $F$ such that, for a fixed point $x_0$ and a given matrix $M_0$, $F(M, x_0)$ is tangential to a convex or concave operator at $M_0$. We establish partial $C^{2,α}$ regularity for equations exhibiting this property. In the second scenario, we establish new partial $W^{2, \\text{VMO}}$ regularity provided that the oscillation of $F$ in $x$ under the $L^n$-norm is of order $o(\\log^{-1}(1/r))$. We address the Hausdorff dimensions of the singular sets of solutions for equations of the form $F(D^2u)=f(x)$ with data $f$ in $W^{1,n}$. Additionally, we demonstrate that the tangent operator property holds for various classes of equations, including nondifferentiable twisted elliptic equations, infimum of $C^1$ equations, semiconvex equations, and piecewise differentiable equations. Finally, we tackle the issue of smooth enveloping and obtain partial regularity of solutions for three subclasses of Isaacs equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00137",
  "author_total": 2,
  "authors": [
    {
      "name": "Cristian E. Gutiérrez"
    },
    {
      "name": "Qingbo Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/959v3pw3z2acb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00137",
  "fulltext_url": null,
  "id": "959v3pw3z2acb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00137",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00137",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/959v3pw3z2acb.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00137",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00137"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Partial $C^{2,α}$ and $W^{2, VMO}$ regularity for nondifferentiable fully nonlinear elliptic equations and Isaacs equations",
  "title_text": "Partial C^2,α and W^2, VMO regularity for nondifferentiable fully nonlinear elliptic equations and Isaacs equations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/959v3pw3z2acb",
  "venue": "arXiv",
  "versions": []
}