We investigate the asymptotic behaviour, as $\epsilon \to 0$, of a class of monotone nonlinear Neumann problems, with growth $p-1$ ($p\in ]1,+\infty [$), on a bounded multidomain ${\Omega}_{\epsilon}\subset {\mathbb{R}}^{N}$
$(N\ge 2)$. The multidomain ${\Omega}_{\epsilon}$ is composed of two domains. The first one is a plate which becomes asymptotically flat, with thickness ${h}_{\epsilon}$ in the ${x}_{N}$ direction, as $\epsilon \to 0$. The second one is a “forest” of cylinders distributed with $\epsilon $-periodicity in the first $N-1$ directions on the upper side of the plate. Each cylinder has a small cross section of size $\epsilon $ and fixed...

We investigate the
asymptotic behaviour,
as ε → 0, of a class of monotone
nonlinear Neumann problems, with growth -1
( ∈]1, +∞[), on a bounded
multidomain
${\Omega}_{\epsilon}\subset {\mathbb{R}}^{N}$ ( ≥ 2). The multidomain
Ω is
composed of two domains. The first one
is a plate which becomes
asymptotically flat, with thickness
h in the
direction, as ε → 0.
The second one
is a “forest" of cylinders
distributed with
-periodicity in the first - 1 directions
on the upper side of the plate.
Each cylinder has
...

We study the asymptotic behaviour
of the following nonlinear problem:
$$\{\begin{array}{c}-\mathrm{div}\left(a\left(D{u}_{h}\right)\right)+{\left|{u}_{h}\right|}^{p-2}{u}_{h}=f\phantom{\rule{1.0em}{0ex}}\text{in}\phantom{\rule{4.0pt}{0ex}}{\Omega}_{h},a\left(D{u}_{h}\right)\xb7\nu =0\phantom{\rule{1.0em}{0ex}}\text{on}\phantom{\rule{4.0pt}{0ex}}\partial {\Omega}_{h},\hfill \end{array}.$$
in a domain Ω_{
h
} of ${\mathbb{R}}^{n}$
whose boundary ∂Ω_{
h
}
contains an oscillating part with respect to h
when h tends to ∞.
The oscillating boundary is defined
by a set of cylinders with axis 0...

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