  Recent work on the quantization of Maxwell theory has used a non-covariant
class of gauge-averaging functionals which include explicitly the effects of
the extrinsic-curvature tensor of the boundary, or covariant gauges which,
unlike the Lorentz case, are invariant under conformal rescalings of the
background four-metric. This paper studies in detail the admissibility of such
gauges at the classical level. It is proved that Euclidean Green functions of a
second- or fourth-order operator exist which ensure the fulfillment of such
gauges at the classical level, i.e. on a portion of flat Euclidean four-space
bounded by three-dimensional surfaces. The admissibility of the axial and
Coulomb gauges is also proved.
