Comptes Rendus
no. 12
Partial Differential Equations
Some uniform elliptic estimates in a porous medium

Presented by: Pierre-Louis Lions

Nader Masmoudi1, 2
1 Courant Institute of Mathematical Sciences, New York University, Warren Weaver Hall, 251, Mercer Street, New York, NY 10012-1185, USA
2 Ceremade, UMR CNRS 7534, université de Paris IX, place du Maréchal DeLattre de Tassigny, 75775 Paris cedex 16, France
Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 849-854.

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 Lp spaces. The domain ωɛ 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 divv=f.

Dans cette Note, nous présentons des estimations uniformes en ɛ pour des problèmes elliptiques écrits dans un milieu poreux. Le domaine ωɛ 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 divv=f.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.10.007

Nader Masmoudi 1, 2

1 Courant Institute of Mathematical Sciences, New York University, Warren Weaver Hall, 251, Mercer Street, New York, NY 10012-1185, USA
2 Ceremade, UMR CNRS 7534, université de Paris IX, place du Maréchal DeLattre de Tassigny, 75775 Paris cedex 16, France 
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Nader Masmoudi. Some uniform elliptic estimates in a porous medium. Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 849-854. doi : 10.1016/j.crma.2004.10.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.10.007/

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