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.
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