Power series solutions to basic stationary boundary value problems of elasticity

The four basic stationary boundary value problems of elasticity for the Lamé equation in a bounded domain of ℝ³ are under consideration. Their solutions are represented in the form of a power series with non-positive degrees of the parameter ω = 1/ (1 -2σ), depending on the Poisson ratio σ. The "coefficients" of the series are solutions of the stationary linearized non-homogeneous Stokes boundary value problems. It is proved that the series converges for any values of ω outside of the minimal interval with the center at the origin and of radius r ≥ 1, which contains all of the Cosserat eigenvalues.