Continuity and canceling operators of order $n$ on ${\mathbb{R}}^n$

Abstract

We prove that for elliptic and canceling linear differential operators $\mathbb{B}$ of order $n$ on ${\mathbb{R}}^n$, continuity of a map $u$ can be inferred from the fact that $\mathbb{B}u$ is a measure. We also prove strict continuity of the embedding of the space ${\mathrm{BV}}^{\mathbb{B}}({\mathbb{R}}^n)$ of functions of bounded $\mathbb{B}$-variation into the space of continuous functions vanishing at infinity.

arXiv comment16 pages

References in corpus (5)

• On Rank-One Convex Functions that are homogeneous of Degree One
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• Hardy-Sobolev inequalities for vector fields and canceling linear differential operators
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Cited by in corpus (3)

• Critical ${\mathrm{L}}^p$-differentiability of ${\mathrm{BV}}^{\mathbb{A}}$-maps and canceling operators
• A trace inequality for solenoidal charges
• Boundary ellipticity and limiting $L^1$-estimates on halfspaces