{
  "abstract": "Let $u^\\varepsilon$ and $u$ be the convex solutions of \\[ \\det D^2u^\\varepsilon=F(x,x/\\varepsilon),\\qquad \\det D^2u=\\overline F(x) \\] on a bounded convex domain $Ω$, with the same Dirichlet data. Here, $F$ is uniformly positive and periodic in its second variable, and $\\overline F(x)=\\int_{\\mathbb T^n}F(x,y)\\,dy$. For $m=0,1$ and $0<α\\leq1$, we prove \\[ \\|u^\\varepsilon-u\\|_{L^\\infty(Ω)}\\leq C\\varepsilon^{m+α},\\qquad \\forall\\,0<\\varepsilon\\leq1, \\] provided that $u\\in C^{m+2,α}(\\overlineΩ)$ and $F\\in C_x^{m,α}(\\overlineΩ;C_y^{0,γ}(\\mathbb T^n))$ for some $0<γ<1$. Both exponents are optimal in their respective regularity scales. We also establish the $O(\\varepsilon^α)$ rate for locally weighted periodic Borel measures, with constants independent of the distribution of the microscopic measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03269",
  "author_total": 4,
  "authors": [
    {
      "name": "Tianling Jin"
    },
    {
      "name": "YanYan Li"
    },
    {
      "name": "Hung V. Tran"
    },
    {
      "name": "Xushan Tu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ede8vns39zxv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03269",
  "fulltext_url": null,
  "id": "6ede8vns39zxv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03269",
  "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",
      "1703|Advanced Mathematical Modeling in Engineering"
    ]
  ],
  "openalex": "W7220387317",
  "pdf_url": "https://arxiv.org/pdf/2610.03269",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ede8vns39zxv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03269",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03269"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative homogenization of Monge-Ampère equations in periodic media",
  "title_text": "Quantitative homogenization of Monge-Ampère equations in periodic media",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/6ede8vns39zxv",
  "venue": "arXiv",
  "versions": []
}