We review a series of works that address homogenization for partial differential equations with highly oscillatory coefficients. A prototypical setting is that of periodic coefficients that are locally, or more globally perturbed. We investigate the homogenization limits obtained, first for linear elliptic equations, both in conservative and non conservative forms, and next for nonlinear equations such as Hamilton-Jacobi type equations.
@article{SLSEDP_2022-2023____A1_0,
author = {Claude Le Bris},
title = {Defects in homogenization theory},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:2},
pages = {1--17},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2022-2023},
doi = {10.5802/slsedp.157},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.157/}
}
TY - JOUR AU - Claude Le Bris TI - Defects in homogenization theory JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:2 PY - 2022-2023 SP - 1 EP - 17 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.157/ DO - 10.5802/slsedp.157 LA - en ID - SLSEDP_2022-2023____A1_0 ER -
%0 Journal Article %A Claude Le Bris %T Defects in homogenization theory %J Séminaire Laurent Schwartz — EDP et applications %Z talk:2 %D 2022-2023 %P 1-17 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.157/ %R 10.5802/slsedp.157 %G en %F SLSEDP_2022-2023____A1_0
Claude Le Bris. Defects in homogenization theory. Séminaire Laurent Schwartz — EDP et applications (2022-2023), Talk no. 2, 17 p. doi : 10.5802/slsedp.157. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.157/
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