有界域上具有离散全纯核的Koppelman公式与方程

数学物理学报 ›› 2004, Vol. 24 ›› Issue (4): 480-484.

有界域上具有离散全纯核的Koppelman公式与方程

黄玉笙, 林良裕

莆田高等专科学校数学系莆田 351100

厦门大学数学系厦门 361005

出版日期:2004-08-25 发布日期:2004-08-25

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

HUANG Yu-Sheng, LIN Liang-Yu

Online:2004-08-25 Published:2004-08-25

摘要/Abstract

摘要：

D是C^n空间中具有逐块C(1)边界的有界域，该文建立了D上一个具有离散局部全纯核的(0，q)形式的Koppelman积分公式及其相应的方程解的积分表示和它的内闭一致估计式。

关键词: 有界域, 离散核, Koppelman公式

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

中图分类号:

32A25

黄玉笙, 林良裕. 有界域上具有离散全纯核的Koppelman公式与方程[J]. 数学物理学报, 2004, 24(4): 480-484.

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.