Lipschitz continuous dependence of piecewise constant Lamé coefficients from boundary data: the case of non flat interfaces

Abstract

We consider the inverse problem of determining the Lamé moduli for a piecewise constant elasticity tensor $\mathbb{C}={\sum }_j{\mathbb{C}}_j{\chi }_{D_j}$, where $\{D_j\}$ is a known finite partition of the body $\Omega$, from the Dirichlet-to-Neumann map. We prove that Lipschitz stability estimates can be derived under $C^{1,\alpha }$ regularity assumptions on the interfaces.