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Abstract. We give here a variational formulation in H ' (T)/R of the exterior Neumann problem for the Laplace operator using a double layer potential. This formulation is then applied to the construction of a finite element method. Optimal error estimates are given.

We present a new system of boundary integral equations for the free-edge plate. This system expresses an abstract symmetric variational problem posed on the boundary of the plate. In order to obtain this abstract problem, we must set the exterior boundary value problem corresponding to the free-edge plate in a framework of weighted Sobolev spaces. Finally, we take care of the hypersingular kernels appearing in our system of BIEs, by using an abstract technique of integration by parts.