Three problems in the theory of continuous media in polyhedrons

Next problems are considered: the problem of electromagnetic oscillations of a hollow resonator with an ideally conductive boundary; steady-state Stokes equations under conditions of slippery walls; the problem of elasticity theory under the boundary condition of a rigid contact. Formally in polyhedral domains all three problems are the same. It is shown that in an interesting sense such coincidence is realized in convex polyhedrons only. Related effects are discussed.