| 双解析函数的一般复合边值问题关于边界曲线的稳定性 |
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| 引用本文： | 林娟,谢碧华.双解析函数的一般复合边值问题关于边界曲线的稳定性[J].纯粹数学与应用数学,2009,25(4):816-821. |
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| 作者姓名： | 林娟 谢碧华 |
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| 作者单位： | 1. 福建商业高等专科学校基础部,福建,福州,350012
2. 福建师范大学数学与计算机科学学院,福建,福州,350007 |
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| 基金项目： | 福建省自然科学基金，福建省教育厅科技项目 |
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| 摘 要： | 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.
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| 关 键 词： | 双解析函数 复合边值问题 光滑摄动 共形映射 稳定性 |
The stability of the general compound boundary value problem for bianalytic functions about boundary curve |
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| LIN Juan,XIE Bi-hua.The stability of the general compound boundary value problem for bianalytic functions about boundary curve[J].Pure and Applied Mathematics,2009,25(4):816-821. |
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| Authors: | LIN Juan XIE Bi-hua |
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| Institution: | LIN Juan 1,XIE Bi-hua 2 (1.Department of Foundation,Fujian Commercial College,Fuzhou 350012,China,2.College of Mathematics , Computer Science,Fujian Normal University,Fuzhou 350007,China) |
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| Abstract: | 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. |
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| Keywords: | bianalytic functions compound boundary value problem smooth perturbation conformal map ping stability |
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