On inverse problems arising in fractional elasticity

Abstract

We first formulate an inverse problem for a linear fractional Lam\'e system. We determine the Lam\'e 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 Lam\'e system. Our arguments are based on the unique continuation property for the fractional operator as well as the associated Runge approximation property.