  In this paper, motivated by a problem arising in random homogenization
theory, we initiate the study of uniform estimates for the fractional penalized
obstacle problem, $ \Delta^{s}u^{\epsilon} = \beta_{\epsilon} (u^{\epsilon})$.
In particular we consider the penalized boundary obstacle problem, $s =
\frac{1}{2}$, and obtain sharp estimates for the solution independent of the
penalizing parameter $\epsilon$. This is a generalization of a result due to H.
Brezis and D. Kinderlehrer.
