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The \(p\)-Laplacian equation in a rough thin domain with terms concentrating on the boundary. (English) Zbl 1447.35033

The authors employ the concepts of reiterated homogenization and periodic unfolding operator to investigate the asymptotic behavior of the solutions of the \(p\)-Laplacian equation with Neumann boundary conditions posed on a rough thin domain with concentrated terms on the boundary. They distinguish between three (scaling-wise) different situations, namely weak, resonant and high roughness, and then derive effective (upscaled) equations for each case.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35B40 Asymptotic behavior of solutions to PDEs
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
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References:

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