How can I calculate the $D$ field when all the free charge is on a conductor embedded in a dielectric?

Let $K$ be a bounded piece of conductor, embedded in an isotropic, homogeneous, uniform dielectric of permittivity $epsilon$.

Let $ vec r$ be a point in the exterior of the conductor. Let $rho_f$ be the free charge density, where all the free charge is on $K$.

Can I say that $$
vec D(r) = frac{1} {4 pi epsilon }int _{mathbb{R}^3 } frac {rho_{f}left(vec{r},’right)}{|vec{r}-vec{r},’|^2}, d^{3}r’ $$ in this case?

(I think this is true when the curl of $vec P$ vanishes, but I am not sure if this holds in this case since $vec P$ may be discontinuous on the boundary of $K$.)