Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity

Consider a three dimensional piecewise homogeneous anisotropic elastic medium Ω which is a bounded domain consisting of a finite number of bounded subdomains Dα, with each Dα a homogeneous elastic medium. One typical example is a finite element model with elements with curvilinear interfaces for an anisotropic elastic medium. Assuming the Dα are known and Lipschitz, we are concerned with the uniqueness in the inverse boundary value problem of identifying the anisotropic elasticity tensor on Ω from a localized Dirichlet-to-Neumann map given on a part of the boundary ∂Dα₀ ∩ ∂Ω of ∂Ω for a single α0, where ∂Dα₀ denotes the boundary of Dα0. If we can connect each Dα to Dα₀ by a chain of {Dα_i}ⁿ _{i =1} such that interfaces between adjacent regions contain a curved portion, we obtain global uniqueness for this inverse boundary value problem. If the Dα are not known but are subanalytic subsets of R³ with curved boundaries, then we also obtain global uniqueness.