Investigation of Riemann Boundary Value Problem for Half Plane in Weighted Spaces of Analytic Functions

Abstract

The boundary value problems that deal with the piecewise continuous solution of an elliptic system that satisfies a certain jump condition on the curves for a given closed curve or a set of finite non-intersecting curves are Riemann boundary value problems. In the first part of this study, the literature summary on the Riemann boundary value problem, the Riemann boundary value problem for the half plane and the Riemann boundary value problem for the half plane in the weighted spaces are given. In the second chapter, the Riemann boundary value problem for the half-plane in the weighted spaces is established, in the third chapter, Lemmas, which are the results obtained for the solution of the problem, are given together with their proofs, and finally, in the fourth chapter, two theorems and their proofs that indicate the necessary and sufficient conditions for the solution of the problem are given.