Riemann Boundary Value Problem with Square Roots on an Open Arc

【摘要】 The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a clas-sical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary func-tion ω (z)is introduced. With different choices of ω (z)’s, some interesting examples are illustrated.更多还原

【Abstract】 The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a clas-sical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary func-tion ω (z)is introduced. With different choices of ω (z)’s, some interesting examples are illustrated.更多还原