ON THE SMOOTHNESS OF THE SOLUTION OF MULTIDIMENSIONAL WEAKLY SINGULAR INTEGRAL-EQUATIONS

Estimates are given for the derivatives of solutions of the integral equation u(x) = integral G K(x, y)u(y) dy + f(x), x is-a-member-of G, where G subset-of R(n) is an open bounded set, the kernel K(x, y) has continuous derivatives up to order m on (G x G)/{x = y}, and there exists a nu (-infinity < nu < n) such that [GRAPHICS] Two weighted function classes are distinguished such that if the free term f is in one of them, so is the solution. The main qualitative consequence is that the tangential derivatives of a solution behave essentially better than the normal derivatives when f is smooth.