关键词: 间断黎曼-希尔伯特问题, 解析函数, 椭圆型复方程

Abstract: It is known that the Keldych-Sedov formula gives the representation of solutions of the mixed boundary value problem for analytic functions in the upper half-plane the authors. But for many problems in mechanics and physics, one needs the more general formula of solutions of discontinuous Riemann-Hilbert boundary value problem for analytic functions in the upper half-plane and other special domains. In the present paper, the authors establish the representations of the general discontinuous boundary value problem for analytic functions in the upper half-plane and upper half-disk. Moreover the authors give their applications to some nonlinear elliptic complex equations. The results in present paper have the important applications to the equations of mixed type and nonlinear mechanics.

Key words: Discontinuous Riemann-Hilbert problem, analytic functions, elliptic complex equations