Problem of Conjugation of Solutions of the Lame Wave Equation in Domains with Piecewise-Smooth Boundaries

We study the problem of conjugation of solutions of the Lame wave equation in domains containing singular lines (sets of angular points) and conic points. We show that solutions of the Lame wave equation have power-type singularities near nonsmoothnesses of boundary surfaces and determine their asymptotics. Taking these asymptotics into account and using the introduced simple-layer, double-layer, and volume elastic retarded potentials, we reduce the problem to a system of functional equations and formulate conditions for its solvability.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 32–46, January, 2005.