TITLE

# A note on equi-integrability in dimension reduction problems

AUTHOR(S)
Braides, Andrea; Zeppieri, Caterina
PUB. DATE
June 2007
SOURCE
Calculus of Variations & Partial Differential Equations;Jun2007, Vol. 29 Issue 2, p231
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
In the framework of the asymptotic analysis of thin structures, we prove that, up to an extraction, it is possible to decompose a sequence of â€˜scaled gradientsâ€™ $${\left(\nabla_\alpha u_\varepsilon\big|\frac{1}{\varepsilon}\nabla_\beta u_\varepsilon\right)}$$ (where $$\nabla_\beta$$ is the gradient in the k-dimensional â€˜thin variableâ€™ x Î²) bounded in $${L^p(\Omega;\mathbb{R}b^{m\times n})}$$ (1 < p < + âˆž) as a sum of a sequence $${\left(\nabla_\alpha v_\varepsilon\big|\frac{1}{\varepsilon}\nabla_\beta v_\varepsilon\right)}$$ whose p-th power is equi-integrable on Î© and a â€˜restâ€™ that converges to zero in measure. In particular, for k = 1 we recover a well-known result for thin films by Bocea and Fonseca (ESAIM: COCV 7:443â€“470; 2002).
ACCESSION #
24476003

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