Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some homogenization and corrector results for nonlinear monotone
  operators   This paper deals with the limit behaviour of the solutions of quasi-linear
equations of the form \ $\ds -\limfunc{div}\left(a\left(x, x/{\varepsilon
_h},Du_h\right)\right)=f_h$ on $\Omega $ with Dirichlet boundary conditions.
The sequence $(\varepsilon _h)$ tends to $0$ and the map $a(x,y,\xi )$ is
periodic in $y$, monotone in $\xi $ and satisfies suitable continuity
conditions. It is proved that $u_h\rightarrow u$ weakly in $H_0^{1,2}(\Omega
)$, where $u$ is the solution of a homogenized problem \
$-\limfunc{div}(b(x,Du))=f$ on $\Omega $. We also prove some corrector results,
i.e. we find $(P_h)$ such that $Du_h-P_h(Du)\rightarrow 0$ in $L^2(\Omega
,R^n)$.

24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc