This article is cited in 7 papers

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

S. D. Troitskaya


Abstract: 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.

UDC: 517.43

MSC: Primary 35L45, 35L50, 35L30, 35L35, 35P05, 76U05; Secondary 35B15, 35A30

Received: 11.03.1993

 English version: Russian Academy of Sciences. Izvestiya Mathematics, 1995, 45:1, 97–124

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