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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 36
  3. Calculus of Variations and Partial Differential Equations : Volume 36, Issue 4, December 2009
  4. Scale-integration and scale-disintegration in nonlinear homogenization
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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 36, Issue 4, December 2009
Symmetry and monotonicity of least energy solutions
A threshold phenomenon for embeddings of $${H^m_0}$$ into Orlicz spaces
Estimates for eigenvalues of the poly-Laplacian with any order in a unit sphere
Positive mass theorem for the Paneitz–Branson operator
Optimal regularity for the Signorini problem
Example of a displacement convex functional of first order
Scale-integration and scale-disintegration in nonlinear homogenization
Linking solutions for quasilinear equations at critical growth involving the “1-Laplace” operator
On global spatial regularity in elasto-plasticity with linear hardening
On derivation of Euler–Lagrange equations for incompressible energy-minimizers
Calculus of Variations and Partial Differential Equations : Volume 36, Issue 3, November 2009
Calculus of Variations and Partial Differential Equations : Volume 36, Issue 2, October 2009
Calculus of Variations and Partial Differential Equations : Volume 36, Issue 1, September 2009
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 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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Scale-integration and scale-disintegration in nonlinear homogenization

Content Provider SpringerLink
Author Visintin, Augusto
Copyright Year 2009
Abstract This work is devoted to scale transformations of stationary nonlinear problems. A class of coarse-scale problems is first derived by integrating a family of two-scale minimization problems (scale-integration), in presence of appropriate orthogonality conditions. The equivalence between the two formulations is established by showing that conversely any solution of the coarse-scale problem can be represented as the fine-scale average of a solution of the two-scale problem (scale-disintegration). This procedure may be applied to the homogenization of several quasilinear problems, and is related to De Giorgi’s notion of Γ-convergence. As an example the homogenization of a simple nonlinear model of magnetostatics is illustrated: a two-scale minimization problem is first derived via Nguetseng’s notion of two-scale convergence, and afterwards the equivalence with a coarse-scale problem is proved.
Ending Page 590
Page Count 26
Starting Page 565
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 4
Volume Number 36
Language English
Publisher Springer-Verlag
Publisher Date 2009-04-29
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Homogenization; equations in media with periodic structure Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Theoretical, Mathematical and Computational Physics Analysis Homogenization Variational methods including variational inequalities Electromagnetic theory, general
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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