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.
Citation
Tomasz Ciaś. "Right inverses for partial differential operators on spaces of Whitney functions." Bull. Belg. Math. Soc. Simon Stevin 21 (1) 147 - 156, february 2014. https://doi.org/10.36045/bbms/1394544300
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