Non-classical Boundary Value Problem of Theory of Elastic Mixtures for Half-plane

In this paper we consider boundary problem for two-component elastic mixture on half-plane, in case when tangents to components to partial displacements and limits of normal components to partial stress values are given along the boundary. In the neighborhood of infinitely distant point conditions for subsiding (disappearance) of partial displacements and their derivatives are given. The limiting values allow for use of Green Theorem as a tool to prove uniqueness theorem. We use Dirichlet and Neumann representation formulas for boundary problem solutions, in case of half-plane, to solve Laplace equation. Uniqueness theorem is proves with the aid of Greene Theorem. The solution is given as a Poisson formula. Smoothness conditions on boundary data are sufficient to establish convergence of resulting Integrals. Please also note that boundary problems for semi-planes in their various forms are studied in: L.Giorgashvili, D.Metreveli.