Search Results for author: Nakasato

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The p-Laplacian in thin channels with locally periodic rough boundaries

no code implementations14 Dec 2020 Nakasato, J. C., Pereira, M. C

In this work we analyze the asymptotic behavior of the solutions of the $p$-Laplacian equation with homogeneous Neumann boundary conditions set in bounded thin domains as $$R^\varepsilon=\left\lbrace(x, y)\in\mathbb{R}^2:x\in(0, 1)\mbox{ and }0<y<\varepsilon G\left(x,{x}/{\varepsilon}\right)\right\rbrace.$$ We take a smooth function $G:(0, 1)\times\mathbb{R} \mapsto \mathbb{R}$, $L$-periodic in the second variable, which allows us to consider locally periodic oscillations at the upper boundary.

Analysis of PDEs 35B25, 35B40, 35J92

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