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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Parabolic equations with variably partially VMO coefficients

Author: H. Dong
Original publication: Algebra i Analiz, tom 23 (2011), nomer 3.
Journal: St. Petersburg Math. J. 23 (2012), 521-539
MSC (2010): Primary 35K15, 35R05
Published electronically: March 2, 2012
MathSciNet review: 2896169
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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.

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Additional Information

H. Dong
Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912

Keywords: Second-order equations, vanishing mean oscillation, partially VMO coefficients, Sobolev spaces
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
Article copyright: © Copyright 2012 American Mathematical Society

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