Uniqueness and Lipschitz stability for the identification of Lam\'e parameters from boundary measurements

TL;DR

This paper proves that the unknown Lamé parameters inside a 3D body can be uniquely identified and depend Lipschitz continuously on boundary measurements, advancing inverse elasticity problem understanding.

Contribution

It establishes the first Lipschitz stability result for the inverse problem of determining piecewise constant Lamé parameters from boundary data.

Findings

Uniqueness of Lamé parameters from boundary measurements

Lipschitz continuous dependence of parameters on data

Applicable to piecewise constant elasticity models

Abstract

In this paper we consider the problem of determining an unknown pair $\lambda$, $\mu$ of piecewise constant Lam\'{e} parameters inside a three dimensional body from the Dirichlet to Neumann map. We prove uniqueness and Lipschitz continuous dependence of $\lambda$ and $\mu$ from the Dirichlet to Neumann map.