The normal dervative of the double layer potential on polygons and galerkin approximation

The method of Mellin transformation is applied to the normal derivative of the double layer potential on a plane polygon. For the corresponding boundary integral ope¬rator continuity, a Carding inequality, and regularity of the solution are proved in Sobolev spaces. The results are applied to show quasi-optimal asymptotic error estimates for the Galerkin approximation procedure which uses the explicit de¬composition of the solution into singular functions at the corners and a smooth remainder