Mixed Boundary Transmission Problems for the Linear Theory of Elasticity

In previous works ([4-8]), the author studied the general approach to solving mixed boundary, spectral, and initial-boundary transmission problems. In this paper, this approach is applied to the mixed boundary transmission problem of the linear theory of elasticity. On the basis of the corresponding Green formulas the solution of the problem can be represented as the sum of the solutions of auxiliary problems containing a given function only in one place. As a result, four auxiliary problems are obtained. We find their weak solutions using Green's formulas. And then we conclude that the solution of the original problem is the sum of the auxiliary solutions.