On the Holmgren-John uniqueness theorem for the wave equation with piecewise analytic coefficients

In this paper a uniqueness theorem is proved for the wave equation in the domain Q^2T=Ω×(0,2T), where Ω is a piecewise analytic Riemannian manifold (Riemannian polyhedron). Initial data are assumed to be given on a part Γ₀ × (0, 2T) of the space-time boundary of the cylinder Q^2T, Γ₀. The uniqueness of a weak solution is proved “in the large,” in a domain formed by the corresponding characteristics of the wave equation. Bibliography:24 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 113–136. Translated by T. N. Surkova.