  We prove interior $C^{1,\alpha}$-regularity for solutions \[
  - \Lambda \leq F(D^2 u) \leq \Lambda \] where $\Lambda$ is a constant and $F$
is fully nonlinear, 1-homogeneous, uniformly elliptic.
  The proof is based on a reduction to the homogeneous equation $F(D^2u) = 0$
by a blow-up argument -- i.e. just like what is done in the case of viscosity
solutions $F(D^2 u) = f$ for $f \in L^\infty$.
  However it was not clear to us that the above inequality implies $F(D^2 u) =
f$ for some bounded $f$ (as would be the case for linear equations in
distributional sense by approximation). Nor were we able to find the literature
on $C^{1,\alpha}$-regularity for viscosity inequalities. So we thought this
result might be worth recording.
