The p-Laplacian equation in thin domains: The unfolding approach

In this work we apply the so called Unfolding Operator Method to analyze the asymptotic behavior of the solutions of the p-Laplacian equation with Neumann boundary condition in a bounded thin domain of the type R-epsilon = {(x, y) is an element of R-2 : x is an element of (0, 1) and 0 < y < epsilon g (x/epsilon(alpha))} 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 oscillations at the top boundary. In the three cases we deduce the homogenized limit and obtain correctors. (C) 2020 Elsevier Inc. All rights reserved.