{
  "abstract": "In this paper we obtain sharp exponents in the Aleksandrov-Bakelman-Pucci maximum estimate for linear uniformly elliptic equations with measurable coefficients, originally conjectured by Pucci in 1966 \\cite{Pucci}, together with corresponding sharp results under the more natural quantification of uniform ellipticity in more than two dimensions. The proofs combine a Hessian integral inequality obtained from boundary Morse inequalities with an obstacle argument. The estimates also hold on arbitrary open sets, of finite volume, without regularity assumptions on their boundaries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23596",
  "author_total": 3,
  "authors": [
    {
      "name": "Shibing Chen"
    },
    {
      "name": "Neil S. Trudinger"
    },
    {
      "name": "Xu-Jia Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4sc0014rsj09r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23596",
  "fulltext_url": null,
  "id": "4sc0014rsj09r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23596",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7222961367",
  "pdf_url": "https://arxiv.org/pdf/2610.23596",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4sc0014rsj09r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23596",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23596"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp maximum estimates for linear uniformly elliptic equations with measurable coefficients",
  "title_text": "Sharp maximum estimates for linear uniformly elliptic equations with measurable coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/4sc0014rsj09r",
  "venue": "arXiv",
  "versions": []
}