Solvability of second-order equations with hierarchically partially BMO coefficients
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- by Hongjie Dong PDF
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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.References
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Additional Information
- Hongjie Dong
- Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
- MR Author ID: 761067
- ORCID: 0000-0003-2258-3537
- Email: Hongjie_Dong@brown.edu
- 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.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 493-517
- MSC (2010): Primary 35J15, 35K15, 35R05
- DOI: https://doi.org/10.1090/S0002-9947-2011-05453-X
- MathSciNet review: 2833589