The elastic Calderon problem in three dimensions: do boundary measurements determine smooth isotropic Lame moduli?

Theorem 1.1: on any bounded connected domain $\Omega\subset\mathbb R^3$ with $C^\infty$ boundary, if $\lambda_j,\mu_j\in C^\infty(\overline\Omega)$ satisfy $\mu_j>0$, $3\lambda_j+2\mu_j>0$ and $\Lambda_{\lambda_1,\mu_1}=\Lambda_{\lambda_2,\mu_2}$, then $\lambda_1=\lambda_2$ and $\mu_1=\mu_2$. No analyticity, smallness or prior boundary agreement is assumed. It is a uniqueness theorem for smooth coefficients and full static data only: no reconstruction algorithm, no stability estimate, no partial-data or low-regularity version, and nothing about anisotropic elasticity.

Theorem 1.1: on any bounded connected domain $\Omega\subset\mathbb R^3$ with $C^\infty$ boundary, if $\lambda_j,\mu_j\in C^\infty(\overline\Omega)$ satisfy $\mu_j>0$, $3\lambda_j+2\mu_j>0$ and $\Lambda_{\lambda_1,\mu_1}=\Lambda_{\lambda_2,\mu_2}$, then $\lambda_1=\lambda_2$ and $\mu_1=\mu_2$. No analyticity, smallness or prior boundary agreement is assumed. It is a uniqueness theorem for smooth coefficients and full static data only: no reconstruction algorithm, no stability estimate, no partial-data or low-regularity version, and nothing about anisotropic elasticity.