On reconstruction of Lam\'e coefficients from partial Cauchy data in three dimensions

TL;DR

This paper proves that in three or more dimensions, the Lamé coefficients of an isotropic elastic system can be uniquely reconstructed from partial boundary measurements, assuming one coefficient is close to a constant.

Contribution

It establishes the unique recoverability of both Lamé coefficients from partial boundary data in 3D, under a smallness condition on one coefficient.

Findings

Unique reconstruction of Lamé coefficients from partial data

Validity in three or more dimensions

Requires one coefficient to be close to constant

Abstract

For the isotropic Lam\'e system, we prove in dimensions three or larger that both Lam\'e coefficients are uniquely recovered from partial Cauchy data on an arbitrary open subset of the boundary provided that the coefficient $\mu$ is a priori close to a constant.