Some uniform elliptic estimates in a porous medium

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In this Note, we give uniform elliptic estimates (uniform in ε) for some elliptic problems written in a periodic porous medium (of period ε) in Lp spaces. The domain ωε is obtained by removing a grid of holes of size ε 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 div v = f.

Original languageEnglish (US)
Pages (from-to)849-854
Number of pages6
JournalComptes Rendus Mathematique
Issue number12
StatePublished - Dec 15 2004

ASJC Scopus subject areas

  • General Mathematics


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