一类曲线上Cauchy积分在尖点处奇异性的探究  

Exploration of the singularities of Cauchy integral at the sharp point on a kind of curves

作　　者：贾婕 刘华[1] 边小丽[1] JIA Jie;LIU Hua;BIAN Xiaoli(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：《高师理科学刊》2020年第6期10-15,共6页Journal of Science of Teachers＇College and University

基　　金：天津职业技术师范大学研究生创新基金项目(YC19-37);国家自然科学基金项目(11802208)。

摘　　要：把开口曲线上的Riemann边值问题解在端点处的奇异性结论推广到2条封闭曲线相切相交产生尖点的情形.验证了3条及n条相切相交带尖点曲线上尖点处Cauchy积分具有类似性质,利用合理剖开封闭曲线给出了几类不同性质的积分核在这类多条相切相交曲线上尖点处的奇异性结论.以2条相切相交封闭曲线为例,对曲线上的Riemann边值问题进行求解,得到了该问题解的一般封闭形式,并证明了解在某些特殊情况下在尖点处的奇异性可以抵消.The singularity at the endpoint of the Riemann boundary value problem on opening curves is extended to the case where two tangented closed curves intersect the sharp point.It is verified that the nature of Cauchy integral at the sharp point of 3 and n tangent intersecting curves has similar properties,and the singularity of some integral cores with different properties are given by reasonable opening at the sharp point on these tangent intersecting curves.Taking two tangent intersecting closed curves as an example,the Riemann boundary value problem is solved,the general closed form of the problem solution is obtained,and it is proved that the singularity at the node can be vanish in some special cases.

关 键 词：带尖点曲线 CAUCHY型积分 跳跃问题 典则函数 

分 类 号：O174.5[理学—数学]