Optimal identification of cavities in the Generalized Plane Stress problem in linear elasticity

2020/01/13 by Morassi, Antonino, Rosset, Edi, Vessella, Sergio
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2001.04805

Abstract

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's function, and by using the strong unique continuation at the boundary for a Kirchhoff-Love plate operator under homogeneous Dirichlet conditions, which has been recently obtained in \citel:arv.

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