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

¹ Department of Mathematics, Iowa State University, 400 Carver Hall Ames IA 50011-2064 USA; vika@iastate.edu
² Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914 Japan; myama@ms.u-tokyo.ac.jp

Received: 17 February 2003
Revised: 22 August 2003

Abstract

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.