Construction of Solutions for the First Elasticity Problem for Noncircular Domain

Here we present a method for constructing the solution a simply connected domain with a given smooth boundary by an approximate solution of the Fredholm equation. Consider the problem in the following formulation: given the dislocations at the boundary, one can find the necessary analytical functions with the given values at the boundary of the region. Here we give a mathematically correct base of the method and construct certain examples. In order to approximately construct the analytic functions in a finite simply connected domain we solve a system of Fredholm equations.