Inverse Problems at the Boundary for an Elastic Medium

Abstract

In this paper, it is proven that one can determine the full Taylor series of the elastic tensor of an elastic, isotropic, inhomogeneous medium in all dimensions $n \geq 2$ and for a generic anisotropic elastic tensor in two dimensions by making measurements at the boundary of the medium of the displacement vectors and corresponding stresses. This information is encoded in the so-called Dirichlet-to-Neumann map.