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Keywords:
$\Gamma $-convergence; oscillatory behaviour; Young measure; conjugate functional
$\Gamma $-convergence; oscillatory behaviour; Young measure; conjugate functional
Summary:
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.
References:
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