A note on equi-integrability in dimension reduction problems |
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Authors: | Andrea Braides Caterina Ida Zeppieri |
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Institution: | (1) Dipartimento di Matematica, Università Roma ‘Tor Vergata’, Via della Ricerca Scientifica, 00133 Roma, Italy;(2) Dipartimento di Matematica ‘G. Castelnuovo’, Università di Roma ‘La Sapienza’, Piazzale Aldo Moro 2, 00185 Roma, Italy |
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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 ‘scaled gradients’ (where is the gradient in the k-dimensional ‘thin variable’ x
β) bounded in (1 < p < + ∞) as a sum of a sequence whose p-th power is equi-integrable on Ω and a ‘rest’ 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 7:443–470; 2002).
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Keywords: | Equi-integrability Dimension reduction |
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