The p-Laplacian equation in thin domains: The unfolding approach
José M. Arrieta, Jean Carlos Nakasato, Marcone Corrêa Pereira · Journal of Differential Equations · 2020
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 $R^\varepsilon=\left\lbrace(x,y)\in\mathbb{R}^2:x\in(0,1)\mbox{ and }0 1$ representing respectively weak, resonant and high osillations at the top boundary. In the three cases we deduce the homogenized limit and obtain correctors.