  We show that for any uniformly elliptic fully nonlinear second-order equation
with bounded measurable "coefficients" and bounded "free" term one can find an
approximating equation which has a unique continuous and having the second
derivatives locally bounded solution in a given smooth domain with smooth
boundary data. The approximating equation is constructed in such a way that it
modifies the original one only for large values of the unknown function and its
derivatives.
