Carleman estimates for the non-stationary Lamé system and the application to an inverse problem

Imanuvilov, Oleg Yu.; Yamamoto, Masahiro

ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 1-56.

In this paper, we establish Carleman estimates for the two dimensional isotropic non-stationary Lamé system with the zero Dirichlet boundary conditions. Using this estimate, we prove the uniqueness and the stability in determining spatially varying density and two Lamé coefficients by a single measurement of solution over $(0,T)\times \omega$, where $T>0$ is a sufficiently large time interval and a subdomain $\omega$ satisfies a non-trapping condition.

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