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.
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.
出处
《北京交通大学学报》
CAS
CSCD
北大核心
2010年第3期48-53,共6页
JOURNAL OF BEIJING JIAOTONG UNIVERSITY
基金
国家自然科学基金资助项目(10671200)