Riemann边值问题关于边界曲线的稳定性

On stability of Riemann boundary value problem with respect to path of boundary

讨论了当E为复平面上的有界连通区域且所有已知函数在E上满足H lder条件时 ,Rieman边值问题在边界曲线Γ E发生光滑扰动时的稳定性问题 ,给出了相应的误差估计 ,并建立了收敛性定理 ,且当Riemann边值问题的指标R <0 时提出了扰动拟可解的概念 .

All known functions being Hlder continuous in a connected region EC, we discuss the stability of Riemann boundary value problem when the smooth perturbation of boundary curve occurs,and give the corresponding error estimates. Finally we establish a convergent theorem and put forward a conception of perturbation quasi-solvability when the index of Riemann boundary problem is less than zero.