Inside a dielectric we have: ∇[itex]\cdot[/itex]ε0E = ρbound + ρfree , where ρbound refers to the fact that these charges come from polarization. We can write this as: ∇[itex]\cdot[/itex]ε0E = -∇[itex]\cdot[/itex]P + ρfree where P is the polarization of the material. And combing the two divergence terms we get: ∇[itex]\cdot[/itex]D = ρfree which is Gauss' law for dielectrics which is quite useful sometimes. However wouldn't it only hold for solid, spherically symmetric, dielectrics, where you consider r<R. My speculation comes from the fact that this derivation does NOT consider the bound surface charges than a polarization can result in. This is of course of no problem if you are inside a solid sphere, but I don't see how it wouldn't be a problem in every other case.