On the interior transmission problem in linear elasticity

In this paper we consider the interior transmission problem in linear elasticity. This problem is fundamental in solving the inverse elastic scattering transmission problem concerning the reconstruction of the geometric characteristics of the elastic inclusion via the well-known "sampling method". We formulate the governing differential equations of the problem in dyadic form in order to acquire a symmetric and uniform representation for the underlying elastic fields. The corresponding far-field operator is defined in the appropriate space setting. We also establish the interior transmission problem in the weak sense and consider the case where the non-homogeneous boundary data are generated by a dyadic source point located in the interior domain. Assuming that the inclusion has absorbing behaviour, that is the Lame constants are complex, we prove existence and uniqueness of the weak solution of the interior transmission problem, properties that constitute prerequisites for the applicability of the sampling method.