Identification Problems in Linear Elasticity

Let V be a bounded domain in Rn with C2-boundary and let D be a Lipschitz domain with D;V. We consider the inverse problem determining D.to the system of linear elasticity D m d d qd d.ql d d.D us.s0 inV, i D ij rs ir js D ir js j ˜ where mD sm˜x D qmx Rn_Dand lDslx D qlx Rn_ D. Under the condition on the Lam`e constants l yl˜. mym˜.G0, we show that D is 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