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 $Q^{2T}=\Omega\times(0,2T)$, where $\Omega$ is a piecewise analytic Riemannian manifold (Riemannian polyhedron). Initial data are assumed to be given on a part $\Gamma_0\times(0,2T)$ of the space-time boundary of the cylinder $Q^{2T}$, $\Gamma_0\in\partial\Omega$. The uniqueness of a weak solution is proved “in the large”, in a domain formed by the corresponding characteristics of the wave equation.