The Cauchy Boundary Value Problems on Closed Piecewise Smooth Manifolds in C^n  

作　　者：Liang Yu LIN Chun Hui QIU 

机构地区：[1]School of Mathematical Sciences,Xiamen University [2]Academy of Mathematics and System Science,CAS

出　　处：《Acta Mathematica Sinica,English Series》2004年第6期989-998,共10页数学学报（英文版）

基　　金：Project supported by the National Natural Science Foundation of China;China Postdoctoral Science Foundation(Grants No.10271097 and No.20040350105)

摘　　要：Suppose that D is a bounded domain with a piecewise C 1 smooth boundary in C n . Let ? ∈ C 1+α (?D). By using the Hadamard principal value of the higher order singular integral and solid angle coefficient method of points on the boundary, we give the Plemelj formula of the higher order singular integral with the Bochner–Martinelli kernel, which has integral density ?. Moreover, by means of the Plemelj formula and methods of complex partial differential equations, we discuss the corresponding Cauchy boundary value problem with the Bochner–Martinelli kernel on a closed piecewise smooth manifold and obtain its unique branch complex harmonic solution.Suppose that D is a bounded domain with a piecewise C 1 smooth boundary in C n . Let ? ∈ C 1+α (?D). By using the Hadamard principal value of the higher order singular integral and solid angle coefficient method of points on the boundary, we give the Plemelj formula of the higher order singular integral with the Bochner–Martinelli kernel, which has integral density ?. Moreover, by means of the Plemelj formula and methods of complex partial differential equations, we discuss the corresponding Cauchy boundary value problem with the Bochner–Martinelli kernel on a closed piecewise smooth manifold and obtain its unique branch complex harmonic solution.

关 键 词：Bochner–Martinelli kernel Hadamard principal value Plemelj formula Boundary value problem 

分 类 号：O186.12[理学—数学]