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2021 A classical approach for the $p$-Laplacian in oscillating thin domains
Jean Carlos Nakasato, Marcone Corrêa Pereira
Topol. Methods Nonlinear Anal. 58(1): 209-231 (2021). DOI: 10.12775/TMNA.2021.009

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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Jean Carlos Nakasato. Marcone Corrêa Pereira. "A classical approach for the $p$-Laplacian in oscillating thin domains." Topol. Methods Nonlinear Anal. 58 (1) 209 - 231, 2021. https://doi.org/10.12775/TMNA.2021.009

Information

Published: 2021
First available in Project Euclid: 5 October 2021

Digital Object Identifier: 10.12775/TMNA.2021.009

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.58 • No. 1 • 2021
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