Determining Lamé coefficients by elastic Dirichlet-to-Neumann map on a Riemannian manifold

Abstract

For the Lamé operator ${\mathcal{L}}_{\lambda ,\mu }$ with variable coefficients $\lambda$ and $\mu$ on a smooth compact Riemannian manifold $(M,g)$ with smooth boundary $\partial M$, we give an explicit expression for full symbol of the elastic Dirichlet-to-Neumann map ${\Lambda }_{\lambda ,\mu }$. We show that ${\Lambda }_{\lambda ,\mu }$ uniquely determines partial derivatives of all orders of the Lamé coefficients $\lambda$ and $\mu$ on $\partial M$. Moreover, for a nonempty open subset $\Gamma \subset \partial M$, suppose that the manifold and the Lamé coefficients are real analytic up to $\Gamma$, we prove that ${\Lambda }_{\lambda ,\mu }$ uniquely determines the Lamé coefficients on the whole manifold $\bar{M}$.

arXiv comment18

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