no code implementations • 14 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