The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and p-growth assumptions on the bulk energy, and the assumption that the surface energy satisfies p-growth upper bound, we show that the studied functional has a nontrivial Γ-limit and the corresponding variational problem admits homogenization.
Mots-clés : homogenization, Γ-convergence, perforated medium
@article{COCV_2010__16_1_148_0,
author = {Chiad\`o Piat, Valeria and Piatnitski, Andrey},
title = {$\Gamma $-convergence approach to variational problems in perforated domains with {Fourier} boundary conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {148--175},
publisher = {EDP-Sciences},
volume = {16},
number = {1},
year = {2010},
doi = {10.1051/cocv:2008073},
mrnumber = {2598093},
zbl = {1188.35015},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2008073/}
}
TY - JOUR AU - Chiadò Piat, Valeria AU - Piatnitski, Andrey TI - $\Gamma $-convergence approach to variational problems in perforated domains with Fourier boundary conditions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 148 EP - 175 VL - 16 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2008073/ DO - 10.1051/cocv:2008073 LA - en ID - COCV_2010__16_1_148_0 ER -
%0 Journal Article %A Chiadò Piat, Valeria %A Piatnitski, Andrey %T $\Gamma $-convergence approach to variational problems in perforated domains with Fourier boundary conditions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 148-175 %V 16 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2008073/ %R 10.1051/cocv:2008073 %G en %F COCV_2010__16_1_148_0
Chiadò Piat, Valeria; Piatnitski, Andrey. $\Gamma $-convergence approach to variational problems in perforated domains with Fourier boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 1, pp. 148-175. doi : 10.1051/cocv:2008073. http://www.numdam.org/articles/10.1051/cocv:2008073/
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