Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar least gradient problem: existence, regularity and anisotropic
  case   We show existence of solutions to the least gradient problem on the plane for
boundary data in $BV(\partial\Omega)$. We also provide an example of a function
$f \in L^1(\partial\Omega) \backslash (C(\partial\Omega) \cup
BV(\partial\Omega))$, for which the solution exists. We also show
non-uniqueness of solutions even for smooth boundary data in the anisotropic
case for a nonsmooth anisotropy. We additionally prove a regularity result
valid also in higher dimensions.

26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs