Γ-convergence of functionals on divergence-free fields
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 809-828.

We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γ-limit is also stable under volume constraint and various type of boundary conditions.

DOI : 10.1051/cocv:2007041
Classification : 35E99, 35J99, 49J45
Mots clés : ${\mathcal {A}}$-quasiconvexity, divergence-free fields, $\Gamma $-convergence, homogenization
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     title = {$\Gamma $-convergence of functionals on divergence-free fields},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {809--828},
     publisher = {EDP-Sciences},
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Ansini, Nadia; Garroni, Adriana. $\Gamma $-convergence of functionals on divergence-free fields. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 809-828. doi : 10.1051/cocv:2007041. http://archive.numdam.org/articles/10.1051/cocv:2007041/

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