Preprint

Inserted: 19 nov 2019
Last Updated: 9 dec 2019

Pages: 29
Year: 2019

Abstract:

We establish some of the well-known fine properties of the classical $\mathrm{BV}$-theory for functions of bounded $\mathcal B$-variation, where $\mathcal B[D]$ is a $\mathbb C$-elliptic operator of arbitrary order (some of these properties are also shown to hold for elliptic operators). As a by-product of our results, we establish fine properties for the deviatoric operator $E - \frac{I_n}{n} \mathrm{div}$ in dimensions $n \ge 3$. In addition, we introduce a linearization principle which reduces the treatment of general elliptic operators to the study of first-order elliptic operators which may be of interest for the overall theory of elliptic operators.