双解析函数的一般复合边值问题关于边界曲线的稳定性

The stability of the general compound boundary value problem for bianalytic functions about boundary curve

开口弧段Γ上的双解析函数的Riemann边值问题与单位圆周L上双解析函数的Hilbert边值问题复合而成的一般复合边值问题,当L与Γ发生微小的光滑摄动后,借助于推广的拉甫伦捷夫近似于圆的共形映射,将星形域映为单位圆域,从而得出摄动后的问题的解的表达式,同时讨论了解的稳定性情况,并给出误差估计.

For the general compound boundary value problems combining Riemann boundary value problem for bianalytic functions on an open arc Γ and Hilbert boundary value problem for bianalytic functions on a unit circle L , when smooth perturbation happens for Γ and L , by extending Lavrentjev＇s conformal mapping on a region approximating to a unit disc from a star-like domain onto a unit disc, the authors show the solutions of the perturbed problem. They also discuss the stability of the solutions and give error estimates.