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

Abstract

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