Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On existence and concentration of solutions to a class of quasilinear
  problems involving the $1-$Laplace operator   In this work we use variational methods to prove results on existence and
concentration of solutions to a problem in $\mathbb{R}^N$ involving the
$1-$Laplacian operator. A thorough analysis on the energy functional defined in
the space of functions of bounded variation $BV(\mathbb{R}^N)$ is necessary,
where the lack of compactness is overcome by using the Concentration of
Compactness Principle of Lions.

12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph