On inverse problems arising in fractional elasticity

We first formulate an inverse problem for a linear fractional Lame system. We determine the Lame parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an inverse problem for a nonlinear fractional Lame system. Our arguments are based on the unique continuation property for the fractional operator as well as the associated Runge approximation property.