{
  "abstract": "We give new proofs of interior second derivative estimates for the Monge-Ampère equation and the constant quadratic Hessian equation, based on the two-point maximum principle. The arguments require only one differentiation of the equation. For the Monge-Ampère equation, the inhomogeneous term is assumed to be positive and continuously differentiable. For the quadratic Hessian equation, the estimate holds in every dimension $n\\ge2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15457",
  "author_total": 3,
  "authors": [
    {
      "name": "Jui-Yun Hung"
    },
    {
      "name": "Jiakun Liu"
    },
    {
      "name": "Neil Trudinger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/196954qameyjz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15457",
  "fulltext_url": null,
  "id": "196954qameyjz",
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  "landing_url": "https://arxiv.org/abs/2610.15457",
  "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": "W7221780101",
  "pdf_url": "https://arxiv.org/pdf/2610.15457",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/196954qameyjz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.15457",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15457"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A new approach to interior estimates for fully nonlinear elliptic equations",
  "title_text": "A new approach to interior estimates for fully nonlinear elliptic equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/196954qameyjz",
  "venue": "arXiv",
  "versions": []
}