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

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

2010-08-19

arxiv.org/abs/1008.3374v1

Mathematics

Analysis of PDEs

35 pages, submitted

Scientific paper

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.

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