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 v alue problems (BVP) for steady state oscillations of piecewise homogen eous anisotropic bodies imbedded into an infinite elastic continuum. U niqueness is shown with the help of generalized Sommerfeld-Kupradze ra diation conditions, while existence follows for arbitrary values of th e oscillation parameter by the reduction of the original interface tra nsmission BVPs to equivalent uniquely solvable boundary integral or ps eudodifferential equations on the interfaces. For the basic BVPs, we s how classical regularity and, in addition for the mixed BVPs that the solutions are Holder continuous with exponent alpha is an element of ( 0, 1/2) in the neighbourhood of the curves of discontinuity of the bou ndary and transmission conditions. (C) 1998 Academic Press.