$\Gamma$-convergence of functionals on divergence-free fields
ESAIM: Control, Optimisation and Calculus of Variations, Volume 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 $\Gamma$-convergence. We prove that the $\Gamma$-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the $\Gamma$-limit is also stable under volume constraint and various type of boundary conditions.

DOI: 10.1051/cocv:2007041
Classification: 35E99,  35J99,  49J45
Keywords: $𝒜$-quasiconvexity, divergence-free fields, $\Gamma$-convergence, homogenization
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Ansini, Nadia; Garroni, Adriana. $\Gamma$-convergence of functionals on divergence-free fields. ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 4, pp. 809-828. doi : 10.1051/cocv:2007041. http://www.numdam.org/articles/10.1051/cocv:2007041/

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