奇异积分方程的标准化(英文)  

Normalization of Singular Integral Equations

作　　者：王金平[1] 龚亚方[2] 

机构地区：[1]湖北师范学院数学系,湖北黄石435002 [2]武汉大学数学与统计学院,湖北武汉430072

出　　处：《内蒙古大学学报（自然科学版）》2003年第2期138-141,共4页Journal of Inner Mongolia University：Natural Science Edition

基　　金：湖北省教育厅重大项目 ( 2 0 0 1 Z0 60 0 3 );湖北师范学院博士科研启动基金资助~~

摘　　要：求解φ(x)=W1(x)u(x)属于h0时奇异积分方程的标准化结果已知道,其中u(x)为H lder连续函数.如果解φ(x)要求属于h(1)或h(-1)或h(-1,1)时,在变换φ(x)=W1(x)σ(x)uσ(x)下介绍了奇异积分方程的一种等价方程,但此时uσ(x)不一定是H lder连续的.本文主要是给出一种新的标准化来解决这一问题.The normalization of the singular integral equations has been known if the solution φ is required to belong to the class h 0, at this time,with the transform φ(x)=W 1(x)u(x),u(t) is Holder continuous in [-1,1] 〔1〕 .When φ is required to belong to the function classes h(-1) or h(1) or h(-1,1) 〔3〕 , the normalization of the singular integral equations has been also known with the transform φ(x)=W 1(x)σ(x)u σ(x) 〔2〕 , but u σ(t) may not be Holder continuous.In this paper,a new method is given to solve this problem,which is very useful in applications.

关 键 词：奇异积分方程 指标 标准化 

分 类 号：O175.5[理学—数学]