On non-almost-periodicity of solutions of the Sobolev problem in domains with edges

This paper is devoted to the study of spectral properties of the Sobolev problem on small oscillations of a rotating fluid in domains containing edges, and perhaps conical points. A new method is proposed for investigating “the Dirichlet problem” for a hyperbolic equation in domains with angles. The method is used to get concrete examples of three-dimensional domains for which there exist non-almost-periodic solutions of the Sobolev problem with a Dirichlet boundary condition, and to determine concrete intervals of the purely continuous spectrum of this problem.