Bulletin of the Belgian Mathematical Society - Simon Stevin

Right inverses for partial differential operators on spaces of Whitney functions

Tomasz Ciaś

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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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1394544300

Mathematical Reviews number (MathSciNet)
MR3178536

Zentralblatt MATH identifier
1304.35212

Subjects
Primary: 35E99: None of the above, but in this section 35F05: Linear first-order equations 46E10: Topological linear spaces of continuous, differentiable or analytic functions
Secondary: 46A04: Locally convex Fréchet spaces and (DF)-spaces

Keywords
Spaces of smooth functions linear partial differential equations with constant coefficients

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


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