A Novel Approach for Solving of Task of Outer Environment of the Ellipse

This chapter is related to elasticity equation solution for 2D media in ellipse outer region. It is provided by conventional complex transform of ellipse outer region to outer region of unit circle. The theory of complex variable functions can be used to express tensions and movements; as a result, it is intended to locate these functions under certain circumstances and for them to satisfy specific requirements at boundary areas. We discover two holomorphic functions for the circle's circumference. The purpose of this study is to identify a method for deriving Dirichlet boundary value issues from the first main boundary problem [1] of the elasticity of the ellipse outer region and solving it using Schwarz equations.