Geodesic
Γ-convergence of functionals on divergence-free fields
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 809-828 Cet article a éte moissonné depuis la source Numdam

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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
Keywords: ${\mathcal {A}}$-quasiconvexity, divergence-free fields, $\Gamma $-convergence, homogenization 
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     author = {Ansini, Nadia and Garroni, Adriana},
     title = {$\Gamma $-convergence of functionals on divergence-free fields},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {809--828},
     year = {2007},
     publisher = {EDP-Sciences},
     volume = {13},
     number = {4},
     doi = {10.1051/cocv:2007041},
     mrnumber = {2351405},
     zbl = {1127.49011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007041/}
}
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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

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