General Transmission Problems in the Theory of Elastic Oscillations of Anisotropic Bodies (Basic Interface Problems)

Here we discuss three-dimensional so-called basic and mixed boundary value problems (BVP) for steady state oscillations of piecewise homogeneous anisotropic bodies imbedded into an infinite elastic continuum. Uniqueness is shown with the help of generalized Sommerfeld–Kupradze radiation conditions, while existence follows for arbitrary values of the oscillation parameter by the reduction of the original interface transmission BVPs to equivalent uniquely solvable boundary integral or pseudodifferential equations on the interfaces. For the basic BVPs, we show classical regularity and, in addition for the mixed BVPs that the solutions are Hölder continuous with exponent α ∈ (0, 1/2) in the neighbourhood of the curves of discontinuity of the boundary and transmission conditions.