Right inverses for partial differential operators on spaces of Whitney functions

TL;DR

This paper proves that certain first-order differential operators with constant coefficients on Whitney function spaces over specific compact sets have continuous linear right inverses, advancing the understanding of differential operator invertibility.

Contribution

It establishes the existence of continuous linear right inverses for first-order differential operators with constant coefficients on Whitney function spaces over particular compact sets.

Findings

Existence of continuous right inverses for specified differential operators

Applicable to compact sets with smooth surfaces and specific intersection properties

Advances the theory of invertibility in Whitney function spaces

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.