  Gauge-invariant boundary conditions in Euclidean quantum gravity can be
obtained by setting to zero at the boundary the spatial components of metric
perturbations, and a suitable class of gauge-averaging functionals. This paper
shows that, on choosing the de Donder functional, the resulting boundary
operator involves projection operators jointly with a nilpotent operator.
Moreover, the elliptic operator acting on metric perturbations is symmetric.
Other choices of mixed boundary conditions, for which the normal components of
metric perturbations can be set to zero at the boundary, are then analyzed in
detail. Last, the evaluation of the 1-loop divergence in the axial gauge for
gravity is obtained. Interestingly, such a divergence turns out to coincide
with the one resulting from transverse-traceless perturbations.
