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Algebra i Analiz, 2012, Volume 24, Issue 1, Pages 53–94 (Mi aa1269)  
This article is cited in 33 scientific papers (total in 33 papers)

Research Papers

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

Hongjie Donga, N. V. Krylovb, Xu Lib

a Division of Applied Mathematics, Brown University, Providence, RI, USA
b University of Minnesota, Minneapolis, MN, USA
Full-text PDF (394 kB) Citations (33)
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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.
Keywords: vanishing mean oscillation, fully nonlinear elliptic and parabolic equations, Bellman's equations.
Received: 12.12.2010
English version:
St. Petersburg Mathematical Journal, 2013, Volume 24, Issue 1, Pages 39–69
DOI: https://doi.org/10.1090/S1061-0022-2012-01231-8
Bibliographic databases:
Document Type: Article
Language: English
Citation: Hongjie Dong, N. V. Krylov, Xu Li, “On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains”, Algebra i Analiz, 24:1 (2012), 53–94; St. Petersburg Math. J., 24:1 (2013), 39–69
Citation in format AMSBIB
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    • This publication is cited in the following 33 articles:
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