**M. Basheleishvili, K. Svanadze**

## A New Method of Solving the Basic Plane Boundary Value Problems of Statics of the Elastic Mixture Theory

**abstract:**

The basic plane boundary value problems of statics
of the elastic mixture theory are considered when on the boundary
are given: a displacement vector (the first problem), a stress vector
(the second problem); differences of partial displacements and
the sum of stress vector components (the third problem). A simple
method of deriving Fredholm type integral equations of second order
for these problems is given. The properties of the new operators are
established. Using these operators and generalized Green formulas
we investigate the above-mentioned integral equations and prove the
existence and uniqueness of a solution of all the boundary value
problems in a finite and an infinite domain.