JournalsjemsOnline First21 December 2021

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

  • Antonino Morassi

    University of Udine, Italy
  • Edi Rosset

    University of Trieste, Italy
  • Sergio Vessella

    Università degli Studi di Firenze, Italy
Optimal identification of cavities in the Generalized Plane Stress problem in linear elasticity cover

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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 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)].

Cite this article

Antonino Morassi, Edi Rosset, Sergio Vessella, Optimal identification of cavities in the Generalized Plane Stress problem in linear elasticity. J. Eur. Math. Soc. (2021), published online first

DOI 10.4171/JEMS/1190