{
  "abstract": "This paper establishes an interior $C^2$ estimate for solutions of \\[ σ_2(D^2u)+α(x)σ_1(D^2u)=f(x,u,Du)>0, \\] on the positive branch $Δu>0$, under the assumptions $α\\ge0$ and $D^2α=βI$. Using one extra variable and a quartic correction, the equation is reduced to a quadratic Hessian equation in one higher dimension. The terms involving $D^2u$ cancel, so the interior estimate of Li--Wu \\cite{LW} applies. The gradient-independent case is also treated. Finally, an example shows that an $L^\\infty$ bound on $α$ alone is not enough.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09490",
  "author_total": 2,
  "authors": [
    {
      "name": "C. Y. Ren"
    },
    {
      "name": "X. L. Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2827fxq51wj9k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09490",
  "fulltext_url": null,
  "id": "2827fxq51wj9k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09490",
  "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": "W7220987780",
  "pdf_url": "https://arxiv.org/pdf/2610.09490",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2827fxq51wj9k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09490",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09490"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Interior $C^2$ Estimates for 2-Sum Hessian Equations",
  "title_text": "Interior C^2 Estimates for 2-Sum Hessian Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/2827fxq51wj9k",
  "venue": "arXiv",
  "versions": []
}