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.

References in corpus (3)

• The stability for the Cauchy problem for elliptic equations
• Stable determination of an inclusion in an elastic body by boundary measurements (unabridged)
• On reconstruction of Lamé coefficients from partial Cauchy data in three dimensions

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