  In this work we apply the unfolding operator method to analyze the asymptotic
behavior of the solutions of the $p$-Laplacian equation with Neumann boundary
condition set in a bounded thin domain of the type
$R^\varepsilon=\left\lbrace(x,y)\in\mathbb{R}^2:x\in(0,1)\mbox{ and
}0<y<\varepsilon g\left({x}/{\varepsilon^\alpha}\right)\right\rbrace$ where $g$
is a positive periodic function. We study the three cases $0<\alpha<1$,
$\alpha=1$ and $\alpha>1$ representing respectively weak, resonant and high
osillations at the top boundary. In the three cases we deduce the homogenized
limit and obtain correctors.
