On correct formulations of Lekhnitskij problems (Q1097734)

The author considers the axisymmetric problem to treat the deformation of an elastic half-space with a cylindrical cavity under its own weight. The particular solution of this problem was found by \textit{S. G. Lekhnitskij} [Theory of elasticity of an anisotropic body (1977; Zbl 0467.73012); English translation (1981; Zbl 0467.73011)]. The two formulations for the solution of this problem are presented: In one of them the stress components become finite at infinity in a layer abutting on the boundary of the half-space, and in the other the displacement components. The discussions are extended to the general case of non-symmetric paraboloidal cavities and elastic inclusions.