Geodesic
Carleman estimates for the non-stationary Lamé system and the application to an inverse problem
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 1-56

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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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     author = {Imanuvilov, Oleg Yu. and Yamamoto, Masahiro},
     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},
     volume = {11},
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     year = {2005},
     doi = {10.1051/cocv:2004030},
     mrnumber = {2110612},
     zbl = {1089.35086},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004030/}
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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, Tome 11 (2005) no. 1, pp. 1-56. doi: 10.1051/cocv:2004030

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