Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak Solutions for Singular Quasilinear Elliptic Systems   We investigate the quasilinear elliptic system $-\Delta_{m} u&=u^{-p}v^{-q}$,
$u>0 \quad\mbox{ in } \Omega$, $-\Delta_{m} v&=u^{r}v^{-s}$, $v>0 \quad\mbox{
in }\Omega$,
  $u=v=0 \quad\mbox{ on } \partial{\Omega}$,
  where $\Omega \subset{\mathbb R}^{N}(N\geq 1)$ is a bounded and smooth
domain, $1<m<\infty, p, q, r, s>0$. Under certain conditions imposed on the
exponents we obtain the existence and uniqueness of a weak solution $(u, v)$
with $u, v \in W_{0}^{1, m}(\Omega)\cap C(\Omega)$. We also investigate the
$W_{0}^{1, \tau}(\Omega)$ regularity of solution and determine the optimal
range of $\tau \geq m$ for such regularity.

30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int