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PreprintCC BY-SA 4.0arXiv

On an inverse boundary problem in elastodynamics

  • Lu Chen
  • Yan Jiang
  • Hongyu Liu
  • Longyue Tao
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Abstract

We study the simultaneous identification of the Lamé parameters λ and μ in three-dimensional static isotropic elasticity. For smooth coefficients, we establish uniqueness from the full Dirichlet-to-Neumann map when μ is axisymmetric, admits a multiplicative or additive separation on a product domain, or is quasianalytic in one fixed direction. These results require neither smallness of ∇μ nor real analyticity of the coefficients, and impose no corresponding structural condition on λ. In the axisymmetric and separated cases, partial boundary data suffice to determine μ.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026inverse,
  title = {{On an inverse boundary problem in elastodynamics}},
  author = {Lu Chen and Yan Jiang and Hongyu Liu and Longyue Tao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20134},
  eprint = {2609.20134},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20134},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - On an inverse boundary problem in elastodynamics
AU  - Lu Chen
AU  - Yan Jiang
AU  - Hongyu Liu
AU  - Longyue Tao
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20134
UR  - https://arxiv.org/abs/2609.20134
AB  - We study the simultaneous identification of the Lamé parameters λ and μ in three-dimensional static isotropic elasticity. For smooth coefficients, we establish uniqueness from the full Dirichlet-to-Neumann map when μ is axisymmetric, admits a multiplicative or additive separation on a product domain, or is quasianalytic in one fixed direction. These results require neither smallness of ∇μ nor real analyticity of the coefficients, and impose no corresponding structural condition on λ. In the axisymmetric and separated cases, partial boundary data suffice to determine μ.
ER  -