document: Solution of a class of two-dimensional integral equations The two-dimensional integral equation 1 / pi integral integral / sub D / -LRB- phi -LRB- r , theta -RRB- / R/sup 2 / -RRB- dS = f -LRB- r/sub 0 / , theta / sub 0 / -RRB- defined on a circular disk D : r/sub 0 / < or = a , 0 < or = theta / sub 0 / < or = 2 pi , is considered in the present paper . Here R in the kernel denotes the distance between two points P -LRB- r , theta -RRB- and P/sub 0 / -LRB- r/sub 0 / , theta / sub 0 / -RRB- in D , and 0 < alpha < 2 or 2 < alpha < 4 . Based on some known results of Bessel functions , integral representations of the kernel are established for 0 < alpha < 2 and 2 < alpha < 4 , respectively , and employed to solve the corresponding two-dimensional integral equation . The solutions of the weakly singular integral equation for 0 < alpha < 2 and of the hypersingular integral equation for 2 < alpha < 4 are obtained , respectively
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