  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 $L^2(\Omega
,R^n)$.
