**L. Giorgashvili, G. Karseladze, G. Sadunishvili**

##
Solution of a Boundary Value Problem of Statics of Two-Component Elastic
Mixtures for a Space with Two Nonintersecting Spherical Cavities

**abstract:**

Using a general representation of solutions of a system of homogeneous
differential equations of statics of two-component elastic mixtures which is
expressed by six harmonic functions, we study boundary value problems of statics
of two-component elastic mixtures for a space with two nonintersecting spherical
cavities when different boundary conditions are given on the spherical surfaces.
The uniqueness theorems are proved. The solution of the considered problems is
reduced to the investigation of an infinite system of linear algebraic
equations. It is proved that such systems are quasiregular. The question of
regularity of the partial displacement vector is studied.

**Mathematics Subject Classification:**
35J55, 75H20, 74H25

**Key words and phrases:** Elasticity theory, theory of mixtures, Green's
formula, regular functions