  We investigate a class of n-dimensional free boundary elliptic problems which
includes the dam problem, the aluminum problem, and the lubrication problem. We
establish that the free boundary in this class is a porous set, which implies
its Hausdorff dimension being less than $n$, which in turn leads to its
Lebesgue measure being zero. Our proof relies on the comparison of the solution
with an appropriately constructed barrier function.
