| 柯西型积分和平面上边值问题 |
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| 引用本文： | 郑神州,舒连清.柯西型积分和平面上边值问题[J].北方交通大学学报,2010(3):48-53. |
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| 作者姓名： | 郑神州 舒连清 |
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| 作者单位： | [1]北京交通大学理学院,北京100044 [2]台州学院信息工程学院,浙江临海 317000 |
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| 基金项目： | 国家自然科学基金资助项目（10671200） |
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| 摘 要： | 综述平面各种边值问题的发展状况：以Cauchy型主值奇异积分为主线,用Plemelj公式求解基本的依跳跃问题,然后从齐次Riemann边值问题的解公式和典则函数得到非齐次Riemann边值问题的解;将Hilbert边值问题化为Riemann边值问题求解.进一步对周期、双周期、群不变的边值、带位移边值及它们相互之间的复合等各种问题,提供转化为典型问题的进展和文献.
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| 关 键 词： | 柯西型积分 Riemann边值问题 Hilbert边值问题 周期边值问题 带位移边值问题 |
Integral of Cauchy Type and Various Boundary-Value Problems in Plane |
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| ZHENG Shenzhou,SHU Lianqing.Integral of Cauchy Type and Various Boundary-Value Problems in Plane[J].Journal of Northern Jiaotong University,2010(3):48-53. |
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| Authors: | ZHENG Shenzhou SHU Lianqing |
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| Institution: | 1.School of Science,Beijing Jiaotong University,Beijing 100044,China;2.School of Information and Technology,Taizhou College,Linhai Zhejiang,317000,China) |
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| Abstract: | We provide the theory and development for various boundary-value problems in the plane.By Starting from a integral of Cauchy type and Plemelj formula,we in turn establish these solutions of jump boundary-value problem,homogeneous Riemann＇s problem and Riemann＇s problem defined in a planar simple domain.Then we can transform famous Hilbert＇s problem into Riemann＇s problem by means of a symmetric expansion w.r.t.the unit circle.Finally,we present the literatures and developments for these boundary value problem of period,double period,invariant Mobius＇s group and their compostions each other. |
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| Keywords: | integral of cauchy type Riemann＇s boundary-value problem Hilbert＇s problem periodic problem boundary-value problem with shift function |
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