Lipschitz continuous dependence of piecewise constant Lam\'e coefficients from boundary data: the case of non flat interfaces

TL;DR

This paper establishes Lipschitz stability estimates for the inverse problem of determining piecewise constant Lamé coefficients from boundary data, assuming interfaces are sufficiently smooth.

Contribution

It provides the first Lipschitz stability results for Lamé coefficients with non-flat interfaces under $C^{1,eta}$ regularity.

Findings

Lipschitz stability estimates are proven for the inverse elasticity problem.

Stability results hold under $C^{1,eta}$ regularity assumptions on interfaces.

The approach extends previous flat interface results to more general geometries.

Abstract

We consider the inverse problem of determining the Lam\'e 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.