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

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