Carleman Estimates for the Three-Dimensional Nonstationary Lame´ System and Application to an Inverse Problem

Abstract In this chapter, we establish Carleman estimates for the three-dimensional isotropic nonstationary Lame´ system with homogeneous Dirichlet boundary conditions. Using this estimate, we prove the uniqueness and stability in determining spatially varying density and two Lame´ coefficients by a single measurement of solution over (0, T ) × ω, where T > 0 is sufficiently large and the subdomain ω satisfies a geometric condition.