On the application of orthogonal polynomials in the theory of elasticity

The first section deals with the questions connected with the definition of a stress-deformed state of isotropic elastic media for linear problems of elasticity in the domain Ω= Ω4 U Ω 2, when Ω1 = D(X Y) x (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar h$$ \end{document}(x, y),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathop h\limits^ +$$ \end{document}(x,y)) mes Ω2 is small. The Schwarz method is used. In the domain Ω2 the problem is solved by the shooting method. In the domain Ω4, depending on h, different orthogonal systems are chosen and, on account of the projection method, the initial problem is approximated by a finite system of multipointed equations defined in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar D$$ \end{document} . The algorithm is proposed by which the finding of the solution of multipointed equations is reduced to a successive solution of a series of differential problems with three unknown functions. In the case when h, is finite the multipointed system is equivalent to Vekua's system. In the second section the techniques proposed are used for studying N.N. Yanenko's linear model,corresponding to the Navier-Stokes equation. The paper presents the calculation methods for a class of multi-dimensional linear problems of the mathematical physics, which belong to the scientific trend predetermined by the late academician I.Vekua. 1. The methods for constructing a calculation scheme for a class of multidimensional problems will be illustrated by an example of the basic linear static problems of three-dimensional elasticity of a homogeneous isotropic body. in the case of connected domains Ω = Ω1UΩ2 when Ω4= D (x,y)x (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar h$$ \end{document}(x,y), \docume