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.