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

Dong, Hongjie; Krylov, N.; Li, Xu

doi:10.1090/S1061-0022-2012-01231-8

On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains
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by Hongjie Dong, N. V. Krylov and Xu Li

St. Petersburg Math. J. 24 (2013), 39-69

DOI: https://doi.org/10.1090/S1061-0022-2012-01231-8

Published electronically: November 15, 2012

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Abstract:

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.

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