Kompleks düzlemde Schwarz problemi

This thesis consists of six chapters and the conclusion chapter. In the first chapter, an introduction to the history of boundary value problems, theorems and definitions to be used in the thesis are given. In the second chapter, for the sake of completeness, we review the Schwarz problem given in the unit disc. In the third chapter, we give the unique solution of the Schwarz problem for inhomogeneous Cauchy-Riemann equations and generalized Beltrami equations in a ring domain. In the fourth chapter, we extend the discussion to second-order equations and investigate the unique solution of the Schwarz problem for second-order linear equations in a ring domain. In the fifth chapter, we give the unique solution of the Schwarz problem for higher-order equations and higher-order linear equations in a ring domain. To analyze the unique solution of the Schwarz problem for higher-order linear equations in a ring domain, we also discuss the properties of higher-order operators. In the sixth chapter, we investigate Schwarz problem for nonlinear higher-order equations. In the conclusion chapter, we summarize the research conducted and the key outcomes of this thesis.