Identification problems in linear elasticity

Let Ω be a bounded domain inRⁿwithC²-boundary and letDbe a Lipschitz domain withD⊂Ω. We consider the inverse problem (determiningD) to the system of linear elasticityD_i((μ_D(δ_ijδ_rs+δ_irδ_js)+λ_Dδ_irδ_js)D_ju^s)=0in Ω,where μ_D=μ_χD+μ_χRn\Dand λ_D=λ_χD+λ_χRn\D. Under the condition on the Lamè constants (λ-λ)(μ-μ)≥0, we show thatDis uniquely determined by the complete knowledge of the Dirichlet-to-Neumann map. We also obtain an uniqueness result for the monotone case from one boundary measurement.