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Topological Methods in Nonlinear Analysis

A classical approach for the $p$-Laplacian in oscillating thin domains
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A classical approach for the $p$-Laplacian in oscillating thin domains

Authors

  • Jean Carlos Nakasato https://orcid.org/0000-0002-4727-2586
  • Marcone Corrêa Pereira https://orcid.org/0000-0003-3600-7418

DOI:

https://doi.org/10.12775/TMNA.2021.009

Keywords

$p$-Laplacian, monotone operators, Neumann boundary condition, thin domains, homogenization

Abstract

In this work we study the asymptotic behavior of solutions to the $p$-Laplacian equation posed in a 2-dimensional open set which degenerates into a line segment when a positive parameter $\varepsilon$ goes to zero (a thin domain perturbation). Also, we notice that oscillatory behavior on the upper boundary of the region is allowed. Combining methods from classic homogenization theory and monotone operators we obtain the homogenized equation proving convergence of the solutions and establishing a corrector function which guarantees strong convergence in $W^{1,p}$ for $1< p< +\infty$.

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Published

2021-09-23

How to Cite

1.
NAKASATO, Jean Carlos and PEREIRA, Marcone Corrêa. A classical approach for the $p$-Laplacian in oscillating thin domains. Topological Methods in Nonlinear Analysis. Online. 23 September 2021. Vol. 58, no. 1, pp. 209 - 231. [Accessed 7 July 2025]. DOI 10.12775/TMNA.2021.009.
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Vol 58, No 1 (September 2021)

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Copyright (c) 2021 Jean Carlos Nakasato, Marcone Corrêa Pereira

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This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

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