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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 29
  3. Calculus of Variations and Partial Differential Equations : Volume 29, Issue 2, June 2007
  4. A note on equi-integrability in dimension reduction problems
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 29, Issue 4, August 2007
Calculus of Variations and Partial Differential Equations : Volume 29, Issue 3, July 2007
Calculus of Variations and Partial Differential Equations : Volume 29, Issue 2, June 2007
Capillary Drops: Contact angle hysteresis and sticking drops
A singular perturbation free boundary problem for elliptic equations in divergence form
Uniqueness of selfdual periodic Chern–Simons vortices of topological-type
An approximation result for solutions of Hessian equations
A note on equi-integrability in dimension reduction problems
Two-scale convergence of some integral functionals
Stable embedded minimal surfaces bounded by a straight line
Calculus of Variations and Partial Differential Equations : Volume 29, Issue 1, May 2007
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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A note on equi-integrability in dimension reduction problems

Content Provider SpringerLink
Author Braides, Andrea Zeppieri, Caterina Ida
Copyright Year 2006
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’ $${\left(\nabla_\alpha u_\varepsilon\big|\frac{1}{\varepsilon}\nabla_\beta u_\varepsilon\right)}$$ (where $$\nabla_\beta$$ is the gradient in the k-dimensional ‘thin variable’ x β) bounded in $${L^p(\Omega;\mathbb{R}b^{m\times n})}$$ (1 < p <  + ∞) 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 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).
Ending Page 238
Page Count 8
Starting Page 231
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 2
Volume Number 29
Language English
Publisher Springer-Verlag
Publisher Date 2006-11-10
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Thin films Dimension reduction Membranes Methods involving semicontinuity and convergence; relaxation Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematical and Computational Physics Analysis Equi-integrability Nonlinear elasticity
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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