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

Abstract

For the Lamé operator L λ , μ with variable coefficients λ and µ on a smooth compact Riemannian manifold (M, g) with smooth boundary ∂ M , we give an explicit expression for the full symbol of the elastic Dirichlet-to-Neumann map Λ λ , μ . We show that Λ λ , μ uniquely determines the partial derivatives of all orders of the Lamé coefficients λ and µ on ∂ M . Moreover, for a nonempty smooth open subset Γ ⊂ ∂ M , suppose that the manifold and the Lamé coefficients are real analytic up to Γ, we prove that Λ λ , μ uniquely determines the Lamé coefficients on the whole manifold M ˉ .