Right inverses for partial differential operators on spaces of Whitney functions

Abstract

For v\in R^n let K be a compact set in R^n containing a suitable smooth surface and such that the intersection {tv+x:t\in R}\cap K is a closed interval or a single point for all x\in K. We prove that every linear first order differential operator with constant coefficients in direction v on space of Whitney functions E(K) admits a continuous linear right inverse.