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The \(p\,\)-Laplacian equation in a rough thin domain with terms concentrating on the boundary

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Abstract

In this work, we use reiterated homogenization and unfolding operator approach to study the asymptotic behavior of the solutions of the p-Laplacian equation with Neumann boundary conditions set in a rough thin domain with concentrated terms on the boundary. We study weak, resonant and high roughness, respectively. In the three cases, we deduce the effective equation capturing the dependence on the geometry of the thin channel and the neighborhood where the concentrations take place.

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Authors and Affiliations

  1. Depto. de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, São Paulo, SP, Brazil

    Ariadne Nogueira & Jean Carlos Nakasato

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  1. Ariadne Nogueira
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  2. Jean Carlos Nakasato
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Correspondence to Ariadne Nogueira.

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Nogueira, A., Nakasato, J.C. The \(p\,\)-Laplacian equation in a rough thin domain with terms concentrating on the boundary. Annali di Matematica 199, 1789–1813 (2020). https://doi.org/10.1007/s10231-020-00943-0

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  • DOI: https://doi.org/10.1007/s10231-020-00943-0

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