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

Abstract

Consider a three dimensional piecewise homogeneous anisotropic elastic medium $\Omega$ which is a bounded domain consisting of a finite number of bounded subdomains $D_{\alpha }$, with each $D_{\alpha }$ a homogeneous elastic medium. One typical example is a finite element model with elements with curvilinear interfaces for an ansiotropic elastic medium. Assuming the $D_{\alpha }$ are known and Lipschitz, we are concerned with the uniqueness in the inverse boundary value problem of identifying the anisotropic elasticity tensor on $\Omega$ from a localized Dirichlet to Neumann map given on a part of the boundary $\partial D_{{\alpha }_0}\cap \partial \Omega$ of $\partial \Omega$ for a single ${\alpha }_0$, where $\partial D_{{\alpha }_0}$ denotes the boundary of $D_{{\alpha }_0}$. If we can connect each $D_{\alpha }$ to $D_{{\alpha }_0}$ by a chain of $\{D_{{\alpha }_i}{\}}_{i=1}^n$ such that interfaces between adjacent regions contain a curved portion, we obtain global uniqueness for this inverse boundary value problem. If the $D_{\alpha }$ are not known but are subanalytic subsets of ${\mathbb{R}}^3$ with curved boundaries, then we also obtain global uniqueness.

References in corpus (2)

• Reconstruction of inclusion from boundary measurements
• Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities