Inverse Density Problem for Linear Elasticity: Uniqueness from Local Measurements on a Partially Accessible Boundary

We consider the inverse boundary value problem in an elasticity system.

It is proved that the density function $\rho$ and its derivatives at the boundary can be uniquely determined from the local Cauchy data.

Furthermore, if the density function is analytic, we can uniquely determine the internal buried objects, as well as the unknown boundary and the boundary conditions imposed on it.

Our methods mainly based on a precise characterization for the principal part of the difference between a special first-order singular solution and the fundamental solution in the $H^m$ norm, and the blow-up property for the boundary Sobolev norms of the volume potential corresponding to the fundamental solution.