In this paper we consider linear partial differential operators P(D) with constant coefficients on the space of smooth Whitney functions [epsilon](K) on a given compact set K [subset] [R.

In this paper we consider compact sets K and partial differential operators P(D) such that there exists a continuous linear right inverse [?

We can easily pass from the case of the first order differential operator to partial differential operators of any given order using the following lemma.

c] the algebra of all linear partial differential operator in 2n + 1 independent variables z,[x.

x]) be a linear partial differential operator with constant coefficients on [R.

x],[partial derivative]/[partial derivative]t) be a linear partial differential operator with constant coefficients on [R.

In dealing with the non existence of solutions of partial differential operators it was customary during the last fifty years and it still is to day in larger applications, to appeal to the necessary Hormander condition which guarantees the non existence of solutions on [R.

Let D be the algebra of partial differential operators with variable coefficients on [R.