  Let $K$ be a field of characteristic 0 and $S=K[x_1,\ldots,x_m]/I$ be an
affine domain. Consider $R=S_P$ where $P\in Spec(S)$ such that $R$ is regular.
In this paper we construct a field $F$ which is contained in $R$ such that
  (1) The residue field of $R$ is a finite extension of $F$.
  (2) $D_F(R)$, the ring of $F$-linear differential operators on $R$ is left
and right Noetherian with finite global dimension.
  (3) The Bernstein class of $D_F(R)$ is closed under localization at one
element of $R$.
  We also prove a similar result for $R^h$, the Henselization of $R$. As an
application we prove that $\frac{D_F(R)}{D_F(R)P}\cong E(\kappa(P))$ where
$E(\kappa(P))$ is the injective hull of the residue field of $R$.
