  In this paper we study the asymptotic behavior of the solutions of a class of
nonlinear elliptic problems posed in a 2-dimensional domain that degenerates
into a line segment (a thin domain) when a positive parameter $\varepsilon$
goes to zero. We also allow high oscillating behavior on the upper boundary of
the thin domain as $\varepsilon \to 0$. Combining methods from classic
homogenization theory for reticulated structures and monotone operators we
obtain the homogenized equation proving convergence of the solutions and
establishing a corrector function which guarantees strong convergence in
$W^{1,p}$ for $1<p<+\infty$.
