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 $L^2(\Omega ,R^n)$.
Categories: math.AP