## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Right inverses for partial differential operators on spaces of Whitney functions

Tomasz Ciaś

#### Abstract

For $v\in\mathbb{R}^n$ let $K$ be a compact set in $\mathbb{R}^n$ containing a suitable smooth surface and such that the intersection $\{tv+x:t\in\mathbb{R}\}\cap K$ 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 $\mathcal E(K)$ admits a continuous linear right inverse.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 1 (2014), 147-156.

Dates
First available in Project Euclid: 11 March 2014

https://projecteuclid.org/euclid.bbms/1394544300

Mathematical Reviews number (MathSciNet)
MR3178536

Zentralblatt MATH identifier
1304.35212

#### Citation

Ciaś, Tomasz. Right inverses for partial differential operators on spaces of Whitney functions. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 1, 147--156. https://projecteuclid.org/euclid.bbms/1394544300