Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Neumann problem involving the $p(x)$-Laplacian with $p=\infty$ in a
  subdomain   In this paper we study a non-homogeneous Neumann problem, where the
$p(x)$-Laplacian is involved and $p=\infty$ in a subdomain. By considering a
suitable sequence $p_k$ of bounded variable exponents such that $p_k \to p$ and
replacing $p$ with $p_k$ in the original problem, we prove the existence of a
solution $u_k$ for each of those intermediate ones. We show that the limit of
the $u_k$ exists and after giving a variational characterization of it, in the
part of the domain where $p$ is bounded, we show that it is a viscosity
solution in the part where $p=\infty$. Finally, we formulate the problem of
which this limit function is a solution in the viscosity sense.

16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph