Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monotonicity of solutions to quasilinear problems with a first-order
  term in half-spaces   We consider a quasilinear elliptic equation involving a first order term,
under zero Dirichlet boundary condition in half spaces. We prove that any
positive solution is monotone increasing w.r.t. the direction orthogonal to the
boundary. The main ingredient in the proof is a new comparison principle in
unbounded domains. As a consequence of our analysis, we also obtain some new
Liouville type theorems.

30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th