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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.

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