On fully nonlinear elliptic and parabolic equations in domains with VMO coefficients
Dong, Hongjie, Krylov, N. V., Li, Xu · arXiv (Cornell University) · 2010
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.