| Abstract: |
| We deal with the inverse problem of determining a polyhedral inclusion compactly contained
in an elastic body from boundary measurements of traction and displacement taken on an open portion of the boundary. Both the inclusion and the body are made of homogeneous isotropic material. Under suitable assumptions on the geometry of the unknown inclusion, we prove a constructive Lipschitz stability estimate from the local Dirichlet-to-Neumann map. The main tools of our approach are quantitative estimates of unique continuation, the construction of singular solutions to the Lam\`{e} system, a boundary formula for the Gateaux derivative of the Dirichlet-to-Neumann map with respect to a deformation homotopy, and the determination of a lower bound of this derivative using, among other tools, the Rongved biphase fundamental solution for the Lam\`{e} system. |
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