The p-Laplacian in thin channels with locally periodic rough boundaries
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866917615212953600 |
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| author | Nakasato, J. C. Pereira, M. C. |
| author_facet | Nakasato, J. C. Pereira, M. C. |
| contents | 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. The thin domain situation is established passing to the limit in the solutions as the positive parameter $\varepsilon$ goes to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_07650 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The p-Laplacian in thin channels with locally periodic rough boundaries Nakasato, J. C. Pereira, M. C. Analysis of PDEs 35B25, 35B40, 35J92 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. The thin domain situation is established passing to the limit in the solutions as the positive parameter $\varepsilon$ goes to zero. |
| title | The p-Laplacian in thin channels with locally periodic rough boundaries |
| topic | Analysis of PDEs 35B25, 35B40, 35J92 |
| url | https://arxiv.org/abs/2012.07650 |