Integral equations for transmission problems in linear elasticity

The scattering of elastic waves by a penetrable homogeneous object is described by a system of integral equations for the field and its traction on the boundary of the scatterer.The system contains the operators of the single and double layer potentials, of the traction of the single layer potential, and of .thetraction of the double layer potential.It is a strongly elliptic system of pseudodifferential equations.Therefore every Galerkin scheme for its approximate solution is convergent.For Lipschitz boundaries we show strong ellipticity of the system of boundary integral operators.This implies existence and uniqueness of the solution and quasioptimal error estimates for its Galerkin solutions.