一类特殊曲线上Cauchy积分在尖点处奇异性分析  

Singularity analysis of Cauchy integral at the sharp point on special arcs

作　　者：贾婕 刘华[1] 边小丽[1] JIA Jie;LIU Hua;BIAN Xiao-li(School of Science,Tianjin University of Technology and Education,Tianjin 300222,China)

机构地区：[1]天津职业技术师范大学理学院,天津300222

出　　处：《天津职业技术师范大学学报》2020年第1期26-29,共4页Journal of Tianjin University of Technology and Education

基　　金：国家自然科学基金资助项目(11802208).

摘　　要：针对开口曲线上的Riemann-Hilbert问题的解在端点处的奇异性问题,即对一组含有节点的一特殊曲线,分析了用于表示问题解的Cauchy积分的性质,尤其是针对具体积分表达式和几类不同性质的积分核在节点处的奇异性分析。对2个交叠产生尖点的相切封闭圆周,利用合理割破封闭曲线,讨论了从平面上4种不同位置趋向切点时Cauchy积分的奇异性分布,证明了在某些特殊情况下节点处的奇异性可以抵消。In view of the singularity of the Riemann-Hilbert problem on the opening curve at the endpoint.In this paper,special arcs containing nodes were analyzed to explore the nature of Cauchy integrals which can be used to represent the solution of the problem.Much attention was given to the singularity analysis of the specific integral expression and several different types of integral kernel at the node.With regard to two tangent closed curves overlap to produce sharp point,the paper discusses the singularity of Cauchy integrals when the tangent point is trending from four different positions on the plane.It is demonstrated that the singularity of the sharp point to the arc can vanish in certain special cases.

关 键 词：带尖点曲线 CAUCHY积分 主值分支 

分 类 号：O172.2[理学—数学]