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

Abstract

Consider a three dimensional piecewise homogeneous anisotropic elastic medium $Ω$ which is a bounded domain consisting of a finite number of bounded subdomains $D_α$, with each $D_α$ a homogeneous elastic medium. One typical example is a finite element model with elements with curvilinear interfaces for an ansiotropic elastic medium. Assuming the $D_α$ 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 $\partial D_{α_0}\cap\partialΩ$ of $\partialΩ$ for a single $α_0$, where $\partial D_{α_0}$ denotes the boundary of $ D_{α_0}$. If we can connect each $D_α$ to $D_{α_0}$ by a chain of $\{D_{α_i}\}_{i=1}^n$ such that interfaces between adjacent regions contain a curved portion, we obtain global uniqueness for this inverse boundary value problem. If the $D_α$ are not known but are subanalytic subsets of $\mathbb{R}^3$ with curved boundaries, then we also obtain global uniqueness.