Some uniform elliptic estimates in a porous medium (Q1764092)

The author presents several uniform estimates for some elliptic problems written in a porous medium. The term uniform refers to the size of the cells which is also equal to the size \(\varepsilon\) of the holes. The author defines a porous medium as the periodic repetition of an elementary cell \(\varepsilon\) in a bounded smooth domain \(\omega\). The author studies the Dirichlet problem, the projection operator onto divergence-free vector fields as well as the Stokes operator. The author also presents estimates for the problem \(\text{div}\,v= f\).