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

Abstract

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

AMS(MOS)Classification Numbers:

• 31A25
• 45E99
• 65R20
• 35R05