Optimal identification of cavities in the generalized plane stress problem in linear elasticity (Q2693153)

Summary: For the Generalized Plane Stress (GPS) problem in linear elasticity, we obtain an optimal stability estimate of logarithmic type for the inverse problem of determining smooth cavities inside a thin isotropic cylinder from a single boundary measurement of traction and displacement. The result is obtained by reformulating the GPS problem as a Kirchhoff-Love plate-like problem in terms of the Airy function, and by using the strong unique continuation at the boundary for a Kirchhoff-Love plate operator under homogeneous Dirichlet conditions, which has recently been obtained in [G. Alessandrini et al., Arch. Ration. Mech. Anal. 231 (2019)].