Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The planar Least Gradient problem in convex domains, the case of
  continuous datum   We study the two dimensional least gradient problem in a convex polygonal set
in the plane. We show existence of solutions when the boundary data are
attained in the trace sense. Due to the lack of strict convexity, the classical
results are not applicable. We state the admissibility conditions on the
continuous boundary datum $f$ that are sufficient for establishing an existence
and uniqueness result. The solutions are constructed by a limiting process,
which uses the well-known geometry of superlevel sets of least gradient
functions.

17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc