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

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

Authors: Hongjie Dong, N. V. Krylov and Xu Li
Original publication: Algebra i Analiz, tom 24 (2012), nomer 1.
Journal: St. Petersburg Math. J. 24 (2013), 39-69
MSC (2010): Primary 35K61, 35B65, 35R05
Posted: November 15, 2012
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Abstract: The solvability in the Sobolev spaces $W^{1,2}_p$ , , 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 $W^{2}_p$ , , of the corresponding elliptic boundary-value problem is also obtained.

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