Carleman estimates for the non-stationary Lamé system and the application to an inverse problem
Department of Mathematics, Iowa State University,
400 Carver Hall Ames IA 50011-2064 USA; firstname.lastname@example.org
2 Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914 Japan; email@example.com
Revised: 22 August 2003
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) x ω, where T > 0 is a sufficiently large time interval and a subdomain ω satisfies a non-trapping condition.
Mathematics Subject Classification: 35B60 / 35R25 / 35R30 / 73C02
Key words: Carleman estimate / Lamé system / inverse problem.
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