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.

中文翻译：

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薄域中的 p-Laplacian 方程：展开方法

在这项工作中，我们应用展开算子方法来分析 $p$-Laplacian 方程解的渐近行为，其中 Neumann 边界条件设置在 $R^\varepsilon=\left\lbrace(x ,y)\in\mathbb{R}^2:x\in(0,1)\mbox{ 和 }0 1$ 分别代表顶部边界处的弱、共振和高振荡。在这三种情况下，我们推导出均质化极限并获得校正器。