Displaying similar documents to “The nonlinear membrane model : a Young measure and varifold formulation”

Homogenization of quadratic complementary energies: a duality example

Hélia Serrano (2011)

Mathematica Bohemica

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We study an example in two dimensions of a sequence of quadratic functionals whose limit energy density, in the sense of Γ -convergence, may be characterized as the dual function of the limit energy density of the sequence of their dual functionals. In this special case, Γ -convergence is indeed stable under the dual operator. If we perturb such quadratic functionals with linear terms this statement is no longer true.

The method of Rothe and two-scale convergence in nonlinear problems

Jiří Vala (2003)

Applications of Mathematics

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Modelling of macroscopic behaviour of materials, consisting of several layers or components, cannot avoid their microstructural properties. This article demonstrates how the method of Rothe, described in the book of K. Rektorys The Method of Discretization in Time, together with the two-scale homogenization technique can be applied to the existence and convergence analysis of some strongly nonlinear time-dependent problems of this type.

Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions

Valeria Chiadò Piat, Andrey Piatnitski (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and -growth assumptions on the bulk energy, and the assumption that the surface energy satisfies -growth...

Homogenization of periodic nonconvex integral functionals in terms of Young measures

Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the Γ -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.