On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains

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