一类带约束的二维弱奇异积分方程的解*

本文找出二维弱奇异第一类积分方程作用着约束方程的解p.p=p(r,θ)={2/π2k(φ₀]}√F(r,θ)-c_*(0≤r≤r_*)其中是(s,φ)原点在M(r,θ)的局部极坐标,(r,θ)是原点在O(0,0)的总体极坐标:k和F是给出的连续函数;φ₀是一常数;F(_*,θ)=c_*(常数)是研究域Q的边界围线。所用方法可推广到三维情形。

Solution of a 2-D Weak Singular Integral Equation with Constraint

In this paper, the solution of a 2-D weak singular integral equation of tire first kind subjected to constraint is found and listed p=p(r,θ)={2/π2k(φ₀]}√F(r,θ)-c_*(0≤r≤r_*) where(s,φ)is a local polar coordhrating with orighr at M(r,θ),(r,θ)is the global polar coordinating with origin at O(0,0):k and F are given continuous functions;φ₀ and C are constant;F(r_*,θ)=c_*(const.)is the boundary contour of considering range Q. The method used can be extended to 3-D cases.