{
  "abstract": "We establish global uniqueness for the inverse boundary value problem of three-dimensional time-harmonic isotropic elasticity with smooth real Lamé parameters satisfying strong convexity and a smooth positive mass density. At a fixed known nonzero frequency for which the corresponding Dirichlet problems are uniquely solvable, the full displacement-to-traction map uniquely determines all three coefficients. The proof first recovers the full boundary Taylor expansions of $λ$, $μ$, and $ρ$, and derives an exact Green--Betti identity for a four-component reduction, with the terms involving $W=ω^2ρ$ and $\\nabla W$ retained. Three independent physical polarizations of the rank-three characteristic quotient yield a complete $3\\times3$ matrix of polynomial moment identities. A Cauchy transform construction produces an exact relative transport matrix $H$, normalized to $I_3$ in a common exterior region. Its invertibility follows from the determinant identity $\\det H=\\sqrt{μ_2/μ_1}>0$. Holomorphic dependence on the projective null direction, established by differentiating the transport equation at a fixed physical point, leads to a finite-type rigidity system that determines the Lamé parameters. Finally, products of physical elastic solutions and Fourier uniqueness recover the mass density.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07642",
  "author_total": 4,
  "authors": [
    {
      "name": "Huaian Diao"
    },
    {
      "name": "Yang Dong"
    },
    {
      "name": "Umidjon Durdiev"
    },
    {
      "name": "Weisheng Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ess0bk8spxwg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07642",
  "fulltext_url": null,
  "id": "1ess0bk8spxwg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07642",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07642",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ess0bk8spxwg.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07642",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07642"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Determination of the Lamé parameters and density at a fixed frequency",
  "title_text": "Determination of the Lamé parameters and density at a fixed frequency",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/1ess0bk8spxwg",
  "venue": "arXiv",
  "versions": []
}