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' (del(alpha)u(epsilon)vertical bar(1)/(epsilon)del(beta)u(epsilon)) (where is the gradient in the k-dimensional 'thin variable' x(beta)) bounded in L-p (Omega:R-mxn(1 < p < + infinity) as a sum of a sequence (del(alpha)v(epsilon)vertical bar(1)/(epsilon)del(beta)nu(epsilon)) whose p-th power is equi-integrable on Omega 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).

Braides, A., & Zeppieri, C.I. (2007). A note on equi-integrability in dimension reduction problems. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 29(2), 231-238 [10.1007/s00526-006-0065-6].

A note on equi-integrability in dimension reduction problems

BRAIDES, ANDREA;
2007

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' (del(alpha)u(epsilon)vertical bar(1)/(epsilon)del(beta)u(epsilon)) (where is the gradient in the k-dimensional 'thin variable' x(beta)) bounded in L-p (Omega:R-mxn(1 < p < + infinity) as a sum of a sequence (del(alpha)v(epsilon)vertical bar(1)/(epsilon)del(beta)nu(epsilon)) whose p-th power is equi-integrable on Omega 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).
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
English
Dimension reduction; Equi-integrability
Braides, A., & Zeppieri, C.I. (2007). A note on equi-integrability in dimension reduction problems. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 29(2), 231-238 [10.1007/s00526-006-0065-6].
Braides, A; Zeppieri, C
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/28844
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