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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

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
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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Additional Information

Hongjie Dong
Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
Email: hongjie{\textunderscore}dong@brown.edu

N. V. Krylov
Affiliation: University of Minnesota, 127 Vincent Hall, Minneapolis, Minnesota 55455
Email: krylov@math.umn.edu

Xu Li
Affiliation: University of Minnesota, 127 Vincent Hall, Minneapolis, Minnesota 55455
Email: lixxx489@umn.edu

DOI: http://dx.doi.org/10.1090/S1061-0022-2012-01231-8
PII: S 1061-0022(2012)01231-8
Keywords: Vanishing mean oscillation, fully nonlinear elliptic and parabolic equations, Bellman’s equations
Received by editor(s): December 12, 2010
Published electronically: November 15, 2012
Additional Notes: The first author was partially supported by NSF grant DMS-0800129. The second author was partially supported by NSF grant DMS-0653121.
Article copyright: © Copyright 2012 American Mathematical Society