  We couple the mixed variational problem for the generalized Hodge-Helmholtz
or Hodge-Laplace equation posed on a bounded three-dimensional Lipschitz domain
with the first-kind boundary integral equation arising from the latter when
constant coefficients are assumed in the unbounded complement. Recently
developed Calderon projectors for the relevant boundary integral operators are
used to perform a symmetric coupling. We prove stability of the coupled problem
away from resonant frequencies by establishing a generalized Garding inequality
(T-coercivity). The resulting system of equations describes the scattering of
monochromatic electromagnetic waves at a bounded inhomogeneous isotropic body
possibly having a "rough" surface. The low-frequency robustness of the
potential formulation of Maxwell's equations makes this model a promising
starting point for Galerkin discretization.
