Geodesic
Homogenization of quadratic complementary energies: a duality example
Mathematica Bohemica, Tome 136 (2011) no. 2, pp. 165-173

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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 $\Gamma $-convergence, may be characterized as the dual function of the limit energy density of the sequence of their dual functionals. In this special case, $\Gamma $-convergence is indeed stable under the dual operator. If we perturb such quadratic functionals with linear terms this statement is no longer true.
We study an example in two dimensions of a sequence of quadratic functionals whose limit energy density, in the sense of $\Gamma $-convergence, may be characterized as the dual function of the limit energy density of the sequence of their dual functionals. In this special case, $\Gamma $-convergence is indeed stable under the dual operator. If we perturb such quadratic functionals with linear terms this statement is no longer true.
DOI : 10.21136/MB.2011.141579
Classification : 35B27, 35J20
Keywords: $\Gamma $-convergence; oscillatory behaviour; Young measure; conjugate functional 
Serrano, Hélia. Homogenization of quadratic complementary energies: a duality example. Mathematica Bohemica, Tome 136 (2011) no. 2, pp. 165-173. doi: 10.21136/MB.2011.141579
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