This article is cited in 33 papers

Research Papers

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

Hongjie Dong^a, N. V. Krylov^b, Xu Li<sup>b

a</sup> Division of Applied Mathematics, Brown University, Providence, RI, USA
^b University of Minnesota, Minneapolis, MN, USA

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.

Keywords: vanishing mean oscillation, fully nonlinear elliptic and parabolic equations, Bellman's equations.

Received: 12.12.2010

Language: English

 English version: St. Petersburg Mathematical Journal, 2013, 24:1, 39–69

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