摘要
利用积分变换技巧,作者给出了C^n中闭光滑可定向流形上一个新的Bochner-Martinelli型积分的高阶偏导数的奇异积分的Hadamard主值,获得了高阶奇异积分的Plemelj公式和合成公式,还讨论了相应的变系数线性微分积分方程的正则化,证明其可转化为一类等价的Fredholm方程。并且指出其特征方程当给出一组适当的边值条件时,在L~*中存在唯一解。
By using the technique of integral transformation, the authors give a new
definition of Hadamard principal value of singular integrals of higher order partial
derivatives for the integral of Bochner-Martinelli type on a closed smooth orientable
manifold in C^n. The Plemelj formula and compsite formula of higher order singular
integral are obtained. The regularization of differential singular integral equations with
linear variable coefficients is discussed. The differential singular integral equation can
be transformed into an equivalent Fredholm equation, whose characteristic equation
has an unique solution in L~* under suitable boundary value conditions.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2004年第4期703-710,共8页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金(10271097)
数学天元基金(TY10126033)
福建省自然科学基金(F0110012)