Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of gradient vector fields giving rise to finite Caccioppoli
  partitions   For a finite set $A \subseteq \mathbb{R}^n$, consider a function $u \in
\mathrm{BV}_{\mathrm{loc}}^2(\mathbb{R}^n)$ such that $\nabla u \in A$ almost
everywhere. If $A$ is convex independent, then it follows that $u$ is piecewise
affine away from a closed, countably $\mathcal{H}^{n - 1}$-rectifiable set. If
$A$ is affinely independent, then $u$ is piecewise affine away from a closed
$\mathcal{H}^{n - 1}$-null set.

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess