  We show that for any uniformly parabolic fully nonlinear second-order
equation with bounded measurable "coefficients" and bounded "free" term in any
cylindrical smooth domain with smooth boundary data one can find an
approximating equation which has a unique continuous solution with the first
derivatives bounded and the second spacial derivatives locally bounded. 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 spacial
derivatives.
