An inverse overdetermined problem for a nonhomogeneous elastic medium

We consider a class of overdetermined problems in the theory of elasticity for which load and displacement vectors are specified on a surface. This class of problems arises in the detection of inhomogeneities of inclusion or crack type for a nonhomogeneous medium. On the basis of a previously introduced integral criterion, we prove a theorem on the uniqueness of the determination of the boundaries of inclusions and the elastic characteristics of the inclusions.