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

Hongjie Dong; N. V. Krylov; Xu Li

paper

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

arXiv:1008.3374

Abstract

We prove the solvability in Sobolev spaces $W_{p}^{1, 2}$ , $p > d + 1$ , 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 $W_{p}^{2}$ , $p > d$ , of the corresponding elliptic boundary-value problem is also obtained.

35 pages, submitted