Dans cette Note, nous présentons des estimations uniformes en ɛ pour des problèmes elliptiques écrits dans un milieu poreux. Le domaine est un domaine perforé obtenu aprés l'elimination de trous de largeure ɛ. Nous étudions en particulier le problème de Dirichlet, l'opérateur de projection sur les vecteurs de divergence nulle, et l'opérateur de Stokes. Nous donnons aussi des estimations sur le problème .
In this Note, we give uniform elliptic estimates (uniform in ɛ) for some elliptic problems written in a periodic porous medium (of period ɛ) in spaces. The domain is obtained by removing a grid of holes of size ɛ from a smooth domain ω. In particular, we study the Dirichlet problem, the projection operator onto divergence-free vector fields as well as the Stokes operator. We also give estimates for the problem .
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@article{CRMATH_2004__339_12_849_0, author = {Masmoudi, Nader}, title = {Some uniform elliptic estimates in a porous medium}, journal = {Comptes Rendus. Math\'ematique}, pages = {849--854}, publisher = {Elsevier}, volume = {339}, number = {12}, year = {2004}, doi = {10.1016/j.crma.2004.10.007}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2004.10.007/} }
TY - JOUR AU - Masmoudi, Nader TI - Some uniform elliptic estimates in a porous medium JO - Comptes Rendus. Mathématique PY - 2004 SP - 849 EP - 854 VL - 339 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.10.007/ DO - 10.1016/j.crma.2004.10.007 LA - en ID - CRMATH_2004__339_12_849_0 ER -
Masmoudi, Nader. Some uniform elliptic estimates in a porous medium. Comptes Rendus. Mathématique, Tome 339 (2004) no. 12, pp. 849-854. doi : 10.1016/j.crma.2004.10.007. http://www.numdam.org/articles/10.1016/j.crma.2004.10.007/
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