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

DOI:
https://doi.org/10.1090/S1061-0022-2012-01206-9

Published electronically:
March 2, 2012

MathSciNet review:
2896169

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The -solvability of second-order parabolic equations in nondivergence form in the whole space is proved for . 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 is removed.

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Additional Information

**H. 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/S1061-0022-2012-01206-9

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