  We prove the solvability in Sobolev spaces $W^{1,2}_p$, $p>d+1$, of the
terminal-boundary value problem for a class of fully nonlinear parabolic
equations, including parabolic Bellman's equations, in bounded cylindrical
domains with VMO ``coefficients''. The solvability in $W^{2}_p$, $p>d$, of the
corresponding elliptic boundary-value problem is also obtained.
