有界域上具有离散全纯核的Koppelman公式与方程

Abstract

Abstract:

Let D be a bounded domain with piecewise C(1) boundary in C^n,f∈C(1)(0,q)(D and f∈C(1) (0,q+1)(D The anthors establish a new integral formula of Koppelman of (0,q) form with discrete holomorphic kernels on D (-1)qf=Lη D f-(RηD+BD)af+R)ηD+BD)f,where LηDf,RηDf,BDf,RηD-fare some corresponding integral operators.If -f=0, then u=(-1)q(RηD+BD)f is a local differentiabl solution of the equation u=f in D, and u has an inner closed uniform estimate in D, i.e. ‖u‖L∞≤C‖f‖L∞.

Key words: Bounded domain, Discrete kernel, Koppelman formula, 〖TX-〗  equation

CLC Number:

32A25

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HUANG Yu-Sheng, LIN Liang-Yu. Koppelman Formula with Discrete Holomorphic Kernel and Equation on a Bounded Domain[J].Acta mathematica scientia,Series A, 2004, 24(4): 480-484.

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References

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[3]陈吕萍，林良裕. 有界域上〖TX-〗〖KG*3〗方程的具有离散核的解. 厦门大学学报(自然科学版), 2000，39(6)：733-736

[4]Koppelman W. The Cauchy integral for differential forms. Bull Amer Math Soc, 1967, 73：554-556

[5]Henkin G M, Leiterer J. Theory of functions on complex manifolds. Berlin： AkademieVerlag, 1984

[6]钟同德，黄沙. 多元复分析. 石家庄：河北教育出版社，1990

[7]林良裕。BergmanWeil积分公式的拓广。数学物理学报，1995，15(4)：442-447

[8]蒋勇国，林良裕，阮其华。复双球垒域用“矩形”挖法的Plemelj公式。数学物理学报，2002，22(3)：379-385

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Koppelman Formula with Discrete Holomorphic Kernel and Equation on a Bounded Domain

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