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

Authors: Lin, Liang¹; Qiu, Chun²

Source: Acta Mathematica Sinica, Volume 20, Number 6, November 2004 , pp. 989-998(10)

Publisher: Springer

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Abstract:

Suppose that D is a bounded domain with a piecewise C ¹ smooth boundary in C ⁿ. Let Φ ∈ 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 Φ. 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.

Keywords: Bochner–Martinelli kernel; Hadamard principal value; Plemelj formula; Boundary valueproblem; 32A25; 32A40

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10114-004-0387-2

Affiliations: 1: School of Mathematical Sciences, Xiamen University, Xiamen 361005, P. R. China, 2: School of Mathematical Sciences, Xiamen University, Xiamen 361005, P. R. China, Email: chqiu@jingxian.xmu.edu.cn

Publication date: 2004-11-01