{
  "abstract": "We establish logarithmic stability for the simultaneous recovery of both Lamé parameters in three-dimensional static isotropic elasticity from the full Dirichlet-to-Neumann map. The $L^\\infty(Ω)$ estimate holds uniformly on every fixed bounded $C^{22}$ class of uniformly strongly convex coefficients, without prescribed exterior coefficients, agreement of boundary values or derivatives, or smallness assumptions on material gradients. For every integer $s\\ge2$, we also obtain boundary stability estimates with exponents $(s-q)/s$ for all Cartesian derivatives of orders $0\\le q<s$, where the measurement error $δ$ is the operator-norm discrepancy between the Dirichlet-to-Neumann maps. These exponents are sharp on admissible classes containing a constant material satisfying the a priori inequalities strictly. On such classes, no uniform modulus of continuity exists for boundary derivatives of order $s$. The proof combines an exact four-component reduction with finite-regularity complex geometrical optics constructions, while deriving complete matrix-valued integral identities from the Betti identity for elastic displacements. An amplitude annihilated by the leading physical adjoint lift produces, at the first nonvanishing order, the third polarization in a rank-three characteristic quotient. Holomorphically weighted matrix moments, Cauchy--Plemelj factorization, and a fixed holomorphic projection then yield quantitative control of the relative transport and recovery of both coefficients. Boundary stability estimates and paired extensions transfer the analysis from an auxiliary common-exterior setting to the original measurement domain. The exact-data argument also establishes global uniqueness for $C^{22}$ Lamé parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24053",
  "author_total": 2,
  "authors": [
    {
      "name": "Huaian Diao"
    },
    {
      "name": "Umidjon Durdiev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0x7da9v6pa1s0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24053",
  "fulltext_url": null,
  "id": "0x7da9v6pa1s0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24053",
  "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",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7223007476",
  "pdf_url": "https://arxiv.org/pdf/2610.24053",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0x7da9v6pa1s0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24053",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24053"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Logarithmic Stability for the Inverse Boundary Problem in Three-Dimensional Isotropic Elasticity",
  "title_text": "Logarithmic Stability for the Inverse Boundary Problem in Three-Dimensional Isotropic Elasticity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/0x7da9v6pa1s0",
  "venue": "arXiv",
  "versions": []
}