The Cauchy Boundary Value Problems on Closed Piecewise Smooth Manifolds in C^n
LiangYuLIN, ChunHuiQIU · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2004
Suppose that D is a bounded domain with a piecewise C^1 smooth boundary in C^n. Let ψ∈C^1+α(δD). 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 Boehner-Martinelli kernel, which has integral density ψ. Moreover, by means of the Plemelj formula and methods of complex partial differential equations, we discuss the corresponding Cauehy boundary value problem with the Boehner-Martinelli kernel on a closed piecewise smooth manifold and obtain its unique branch complex harmonic solution.