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Equi-integrability results for 3D-2D dimension reduction problems
Published online by Cambridge University Press: 15 September 2002
Abstract
3D-2D asymptotic analysis for thin structures rests on the mastery
of scaled gradients $\left( \nabla _{\alpha}u_\varepsilon\big|
\frac{1}{\varepsilon}\nabla _3 u_\varepsilon\right) $ bounded in $L^p (\Omega;
\mathbb{R}^9 ), \ 1 < p < +\infty .$
Here it is shown that, up to a
subsequence, $u_\varepsilon$
may be decomposed as $w_\varepsilon+ z_\varepsilon,$
where $z_\varepsilon$
carries all the concentration effects, i.e.$\left\{ \left| \left( \nabla _{\alpha }w_\varepsilon| \frac{1}{\varepsilon
}\nabla _3 w_\varepsilon\right) \right| ^{p} \right\} $
is
equi-integrable, and $w_\varepsilon$
captures the oscillatory behavior,
i.e.$z_\varepsilon\to 0$
in measure. In addition, if $\{ u_\varepsilon\} $
is
a recovering sequence then $z_\varepsilon= z_\varepsilon(x_\alpha )$
nearby
$\partial \Omega.$
Keywords
- Type
- Research Article
- Information
- Copyright
- © EDP Sciences, SMAI, 2002
References
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