Carleman estimates for the non-stationary Lamé system and the application to an inverse problem
ESAIM: Control, Optimisation and Calculus of Variations, Volume 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)×ω, where T>0 is a sufficiently large time interval and a subdomain ω satisfies a non-trapping condition.

DOI: 10.1051/cocv:2004030
Classification: 35B60, 35R25, 35R30, 73C02
Keywords: Carleman estimate, Lamé system, inverse problem
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     title = {Carleman estimates for the non-stationary {Lam\'e} system and the application to an inverse problem},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1--56},
     publisher = {EDP-Sciences},
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Imanuvilov, Oleg Yu.; Yamamoto, Masahiro. Carleman estimates for the non-stationary Lamé system and the application to an inverse problem. ESAIM: Control, Optimisation and Calculus of Variations, Volume 11 (2005) no. 1, pp. 1-56. doi : 10.1051/cocv:2004030. http://www.numdam.org/articles/10.1051/cocv:2004030/

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