关于Green公式若干问题的探讨

An Approach on Some Problems of Green's Formula

本文研究了Green公式的某些问题,讨论了函数P(x,y),Q(x,y)及偏导数 P/ y, Q/ x在有界连通(单连通的或复连通的)区域D内(或边界C上)存在奇点的情形。利用广义积分收敛的定义,在一定条件下,证明了一个新的定理。可以看出,该新定理是Green公式的进一步推广与完善。此外,还讨论了Green公式的两种形式。最后,给出了例子说明定理的应用。

In this paper, some problems of Green's formula are studied. The cases for the existence of singularities of functions P(x,y), Q(x,y) and partial derivatives are discussed in the bounded connected (simply connected or complex connected) region D (or on the boundary C ). A new theorem is proved, using the definition of convergence of improper integral under certain conditions. It is observed that the new theorem is a further extension and perfection of Green's formula. Moreover, two kinds of forms of Green's formula are also discussed. Example for illustrating the application of the theorem is given.