We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of -convergence. We prove that the -limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the -limit is also stable under volume constraint and various type of boundary conditions.
Keywords: ${\mathcal {A}}$-quasiconvexity, divergence-free fields, $\Gamma $-convergence, homogenization
@article{COCV_2007__13_4_809_0,
author = {Ansini, Nadia and Garroni, Adriana},
title = {$\Gamma $-convergence of functionals on divergence-free fields},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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 = {https://www.numdam.org/articles/10.1051/cocv:2007041/}
}
TY - JOUR AU - Ansini, Nadia AU - Garroni, Adriana TI - $\Gamma $-convergence of functionals on divergence-free fields JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 809 EP - 828 VL - 13 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2007041/ DO - 10.1051/cocv:2007041 LA - en ID - COCV_2007__13_4_809_0 ER -
%0 Journal Article %A Ansini, Nadia %A Garroni, Adriana %T $\Gamma $-convergence of functionals on divergence-free fields %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 809-828 %V 13 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2007041/ %R 10.1051/cocv:2007041 %G en %F 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, Tome 13 (2007) no. 4, pp. 809-828. doi: 10.1051/cocv:2007041
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