On the determination of radially dependent Lame coefficients

In this paper, we prove that one can determine radially dependent Lame coefficients lambda and mu 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.