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' (∇αuε|1\ ε∇βuε) (where ∇ β is the gradient in the k-dimensional 'thin variable' x β) bounded in Lp(Ωℝm×n)(1 < p < + ∞) as a sum of a sequence (∇αv ε|1\ε∇βvε) 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). © Springer-Verlag 2007.
A note on equi-integrability in dimension reduction problems / Braides, A.; Zeppieri, C. I.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 29:2(2007), pp. 231-238. [10.1007/s00526-006-0065-6]
A note on equi-integrability in dimension reduction problems
Braides A.;Zeppieri C. I.
2007-01-01
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' (∇αuε|1\ ε∇βuε) (where ∇ β is the gradient in the k-dimensional 'thin variable' x β) bounded in Lp(Ωℝm×n)(1 < p < + ∞) as a sum of a sequence (∇αv ε|1\ε∇βvε) 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). © Springer-Verlag 2007.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
