Abstract
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 radiusr≥1, which contains all of the Cosserat eigenvalues.
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Dedicated to Prof. I.Gohberg on the occasion of his 70th birthday