Some uniform elliptic estimates in a porous medium
Nader Masmoudi · Comptes Rendus Mathématique · 2004
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 L p spaces. The domain ω ɛ 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 div v = f .