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

• Published in: Annali di matematica pura ed applicata Vol. 199; no. 5; pp. 1789 - 1813
• Main Authors: Nogueira, Ariadne, Nakasato, Jean Carlos
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-10-2020; Springer Nature B.V
• Subjects: Asymptotic properties; Boundary conditions; Domains; Laplace equation; Mathematics; Mathematics and Statistics; 35B25; 35J92; Neumann boundary condition; Homogenization; 35B40; Laplacian; Thin domains
• ISSN: 0373-3114; 1618-1891
• DOI: 10.1007/s10231-020-00943-0

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.