Calculus of Variations and Geometric Measure Theory
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B. Raita - A. Skorobogatova

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

created by skorobogatova on 20 Nov 2019

[BibTeX]

preprint

Inserted: 20 nov 2019

Year: 2019

ArXiv: 1903.03574 PDF

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.

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