{
  "abstract": "We study convergence rates when periodic homogenization and vanishing viscosity occur at the same scale in Hamilton--Jacobi equations whose momentum Hessians are positive definite at every point. For bounded Lipschitz initial data and a class of smooth Hamiltonians, we establish an optimal rate $O(\\varepsilon|\\log\\varepsilon|)$ on fixed time intervals. The second-order term plays a key role: the elliptic cell problem provides higher derivative bounds for the effective Hamiltonian $\\bar{H}$ and its Legendre dual $\\bar{L}$. The proof is purely PDE, based on corrector expansions and viscosity comparison, while its guiding idea comes from the control interpretation of the Hopf--Lax formula. For a fixed target $(x,t)$, a minimizing origin selects a characteristic velocity and its dual momentum, these guide the construction of smooth comparison profiles, whose gradients supply the momentum argument of the first-order corrector. Thus we never need to differentiate the effective solution, even at points where it is nonsmooth.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30693",
  "author_total": 1,
  "authors": [
    {
      "name": "Kai Qin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bem7ta36sxm6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30693",
  "fulltext_url": null,
  "id": "7bem7ta36sxm6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30693",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "1703|Advanced Mathematical Modeling in Engineering"
    ]
  ],
  "openalex": "W7214627150",
  "pdf_url": "https://arxiv.org/pdf/2609.30693",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bem7ta36sxm6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30693",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30693"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Convergence rates in the periodic homogenization of vanishing-viscous Hamilton-Jacobi equations",
  "title_text": "Convergence rates in the periodic homogenization of vanishing-viscous Hamilton-Jacobi equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/7bem7ta36sxm6",
  "venue": "arXiv",
  "versions": []
}