On the determination of radially dependent Lame coefficients

In this paper, we prove that one can determine radially dependent Lame coefficients λ and μ of an isotropic elastic ball by choosing only two correspondences in the Dirichlet-to-Neumann map, i.e., twice making measurements of displacement and stress on the surface of the ball. This is a one-dimensional, multiunknown, undetermined coefficient problem for a system of partial differential equations. We use a matrix form of the transmutation mapping for solving this problem. The procedure for proving the uniqueness based on transmutation can be viewed as a computational algorithm. Also the method we develop has the potential of solving other one-dimensional, multiunknown inverse problems.