Parabolic equations with variably partially VMO coefficients
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- by H. Dong
- St. Petersburg Math. J. 23 (2012), 521-539
- DOI: https://doi.org/10.1090/S1061-0022-2012-01206-9
- Published electronically: March 2, 2012
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Abstract:
The $W^{1,2}_{p}$-solvability of second-order parabolic equations in nondivergence form in the whole space is proved for $p\in (1,\infty )$. The leading coefficients are assumed to be measurable in one spatial direction and have vanishing mean oscillation (VMO) in the orthogonal directions and the time variable in each small parabolic cylinder with direction allowed to depend on the cylinder. This extends a recent result by Krylov for elliptic equations. The novelty in the current paper is that the restriction $p>2$ is removed.References
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Bibliographic Information
- H. 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): June 20, 2010
- Published electronically: March 2, 2012
- Additional Notes: Partially supported by NSF Grant DMS-0635607 from IAS and NSF Grant DMS-0800129
- © Copyright 2012 American Mathematical Society
- Journal: St. Petersburg Math. J. 23 (2012), 521-539
- MSC (2010): Primary 35K15, 35R05
- DOI: https://doi.org/10.1090/S1061-0022-2012-01206-9
- MathSciNet review: 2896169