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

• Main Authors: Nogueira, Ariadne, Nakasato, Jean Carlos
• Format: Journal Article
• Language: English
• Published: 22-11-2019
• Subjects: Mathematics - Analysis of PDEs
• DOI: 10.48550/arxiv.1911.10263

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.