We have an infinite half-space filled with a dielectric. The other half-space is vacuum. We take a sheet of charge of density \sigma and place it on the surface of the dielectric. What are the D & E fields everywhere? We clearly have D_1 + D_2 = \sigma. But what other equation do we have? Can we find D_1 & D_2 without knowing the properties of the dielectric? It seems like this should be very simple, but it's tripping me up. I don't think we can claim D_1 = D_2, because we don't have symmetry. Or am I wrong about this?