• Gianni Dal Maso
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 8)


In this chapter we study the Γ-limit, as ε→0+,of a family (F ε)ε>0 of functional of the form
$$ {{F}_{\varepsilon }}(u,A) = \left\{ {\begin{array}{*{20}{c}} {\int_{A} {f(\frac{x}{\varepsilon },Du(x)),ifu \in W_{{loc}}^{{1,1}}(A),} } \hfill \\ { + \infty ,otherwise,} \hfill \\ \end{array} } \right. $$
where f(x,ξ) is convex in ξ and periodic in x. When F ε represents the stored energy of a (possibly nonlinear) inhomogeneous material with a periodic structure, this convergence analysis is related to the so called “homogenization problem”, i.e., the problem of finding the physical properties of a homogeneous material, whose overall response is close to that of the periodic material, when the size ε of the periodicity cell tends to 0.


Open Subset Positive Real Number Convergence Analysis Lower Semicontinuous Homogeneous Material 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Gianni Dal Maso
    • 1
  1. 1.International School for Advanced Studies (SISSA)TriesteItaly

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