Generalized impedance boundary conditions for the Maxwell equations as singular perturbations problems

In this paper the Maxwell equations in an exterior domain with the generali zed impedance boundary conditions of Engquist-Nedelec are considered. The p articular form of the assumed boundary conditions can be considered to be a singular perturbation of the Dirichlet boundary conditions. The convergenc e of the solution of the Maxwell equations with these generalized impedance boundary conditions to that of the corresponding Dirichlet problem is prov en. The proof uses a new integral equation method combined with results dea ling with singular perturbation problems of a class of pseudo-differential operators.