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 elasticityDi((μD(δijδrs+δirδjs)+λDδirδjs)Djus)=0in Ω,where μD=μχD+μχRn\Dand λD=λχD+λχRn\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.
Bibliographical noteFunding Information:
We thank the referee for several comments. The second author is supported in part by GARC-KOSEF, BSRI96-0701-04-01-3, and IMS at Yonsei University.
All Science Journal Classification (ASJC) codes
- Applied Mathematics