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PreprintarXiv licencearXiv

Boundary determination from the anisotropic elastic Dirichlet-to-Neumann map

  • Joonas Ilmavirta
  • Mikko Salo
  • Hjørdis Schlüter
  • Daniel Windisch
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Abstract

We show that the Dirichlet-to-Neumann map of the elastic wave equation determines the density and the anisotropic stiffness tensor on the boundary for generic density and stiffness tensor fields. The proof builds on an interplay between microlocal analysis and algebraic geometry. Microlocal analysis yields a construction of special solutions, valid for many real principal type systems, that concentrate near a boundary point. Generic conditions ensure that this construction holds and allow for extraction of information about stiffness tensor and density at the boundary. We also describe the generic sets through algebraic conditions.

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Cite

BibTeXRIS
BibTeX
@misc{ilmavirta2026boundary,
  title = {{Boundary determination from the anisotropic elastic Dirichlet-to-Neumann map}},
  author = {Joonas Ilmavirta and Mikko Salo and Hjørdis Schlüter and Daniel Windisch},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04856},
  eprint = {2611.04856},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04856},
}
RIS
TY  - UNPB
TI  - Boundary determination from the anisotropic elastic Dirichlet-to-Neumann map
AU  - Joonas Ilmavirta
AU  - Mikko Salo
AU  - Hjørdis Schlüter
AU  - Daniel Windisch
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04856
UR  - https://arxiv.org/abs/2611.04856
AB  - We show that the Dirichlet-to-Neumann map of the elastic wave equation determines the density and the anisotropic stiffness tensor on the boundary for generic density and stiffness tensor fields. The proof builds on an interplay between microlocal analysis and algebraic geometry. Microlocal analysis yields a construction of special solutions, valid for many real principal type systems, that concentrate near a boundary point. Generic conditions ensure that this construction holds and allow for extraction of information about stiffness tensor and density at the boundary. We also describe the generic sets through algebraic conditions.
ER  -