{
  "abstract": "Let $\\mathcal{L}_\\varepsilon=-\\operatorname{div}(A(x/\\varepsilon)\\nabla)$ be a scalar divergence-form operator on a bounded $C^3$ domain, where $A$ is symmetric, uniformly elliptic, Lipschitz continuous, and periodic. For initial data spectrally truncated at the eigenvalue level $N$, we establish whole-boundary observability and projected exact controllability, uniformly in the range $N\\leqδ\\varepsilon^{-1}$. This extends the cutoff $N\\lesssim\\varepsilon^{-1/2}$ obtained by Lin and Shen (J. Eur. Math. Soc. 2022). The key input is a two-sided boundary estimate for fixed-width spectral packets of $\\sqrt{\\mathcal{L}_\\varepsilon}$ at frequencies that satisfy $\\varepsilonμ^2\\ll1$. Its lower bound combines quantitative Dirichlet corrector estimates with a forcing-stable microscopic boundary Cauchy estimate. Miller's spectral packet criterion and the Hilbert uniqueness method then convert this packet estimate into the corresponding wave results, with constants independent of $\\varepsilon$ and $N$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33547",
  "author_total": 3,
  "authors": [
    {
      "name": "Jun Geng"
    },
    {
      "name": "Shumao Wang"
    },
    {
      "name": "Wei Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0y5sf2qby1a6z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33547",
  "fulltext_url": null,
  "id": "0y5sf2qby1a6z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33547",
  "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",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7223810356",
  "pdf_url": "https://arxiv.org/pdf/2610.33547",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0y5sf2qby1a6z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33547",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33547"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniform boundary observability for periodic waves, I: up to the $\\varepsilon^{-1}$ eigenvalue scale",
  "title_text": "Uniform boundary observability for periodic waves, I: up to the ε^−1 eigenvalue scale",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/0y5sf2qby1a6z",
  "venue": "arXiv",
  "versions": []
}