Generalized Impedance Boundary Conditions for the Maxwell Equations as Singular Perturbation Problems

In this paper the Maxwell equations in an exterior domain with the generalized impedance boundary conditions of Engquist-N ed elec are considered. The particular form of the assumed boundary conditions can be considered to be a singular perturbation of the Dirichlet boundary conditions. The convergence of the solution of the Maxwell equations with these generalized impedance boundary conditions to that of the corresponding Dirichlet problem is proven. The proof uses a new integral equation method combined with results dealing with singular perturbation problems of a class of pseudo-diierential operators.