一种特殊曲线上的Hilbert核奇异积分方程

A Kind of Special Curve Singular Intergral Equations with Hilbert Kernel

利用开口弧曲线上Hilbert核奇异积分方程的特点,采用保形映射的方法,把这种特殊的开口弧曲线上的Hilbert核奇异积分方程转化为封闭曲线的情况,并进行了求解,给出了完美的解答。这种方法同样可应用于余割核同类问题的求解,因此具有普遍意义。

In this paper, the characteristics of the singular integral equation with Hilbert kernel on a special open curve and conformal mapping are applied to transform this special equation from open curve to close curve to get perfect solution. The method can also be applied to the solution of singular intergral equation with cosecent.