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Solvability of second-order equations with hierarchically partially BMO coefficients


Author: Hongjie Dong
Journal: Trans. Amer. Math. Soc. 364 (2012), 493-517
MSC (2010): Primary 35J15, 35K15, 35R05
Published electronically: August 25, 2011
MathSciNet review: 2833589
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Abstract: By using some recent results for divergence-form equations, we study the $ L_p$-solvability of second-order elliptic and parabolic equations in nondivergence form for any $ p\in (1,\infty)$. The leading coefficients are assumed to be in locally BMO spaces with suitably small BMO seminorms. We not only extend several previous results by Krylov and Kim to the full range of $ p$, but also deal with equations with more general coefficients.


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Additional Information

Hongjie Dong
Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
Email: Hongjie_Dong@brown.edu

DOI: https://doi.org/10.1090/S0002-9947-2011-05453-X
Keywords: Second-order equations, vanishing mean oscillation, partially BMO coefficients, Sobolev spaces
Received by editor(s): April 30, 2009
Received by editor(s) in revised form: August 22, 2010
Published electronically: August 25, 2011
Additional Notes: The author was partially supported by NSF grant number DMS-0635607 from IAS, and NSF grant number DMS-0800129.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.