Γ-convergence of functionals on divergence-free fields
ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 4, p. 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 : https://doi.org/10.1051/cocv:2007041
Classification:  35E99,  35J99,  49J45
Keywords: 𝒜-quasiconvexity, divergence-free fields, Γ-convergence, homogenization
@article{COCV_2007__13_4_809_0,
     author = {Ansini, Nadia and Garroni, Adriana},
     title = {$\Gamma $-convergence of functionals on divergence-free fields},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {13},
     number = {4},
     year = {2007},
     pages = {809-828},
     doi = {10.1051/cocv:2007041},
     zbl = {1127.49011},
     mrnumber = {2351405},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2007__13_4_809_0}
}
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/item/COCV_2007__13_4_809_0/

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