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ON SOME WEAKLY SINGULAR INTEGRAL EQUATION OF THE FIRST KIND

with weakly singular symmetric kernel was studied by S.Zaremba [5] in connection with some problem of mechanics. S.G.Michlin in the monograph [2] has pointed out the possibility of solving the equation (1) on the basis of the Hilbert-Schmidt theorem. In our paper we shall try to investigate some integral equation with weakly singular, non-symmetric kernel arising in the theory of the Dirichlet problem for the elliptic differential equation with variable coefficients. The problem consists in determining the function u(A), which satisfies the equation