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ISSN 1088-6850(e) ISSN 0002-9947(p)

Second-order elliptic and parabolic equations with $B(\mathbb{R}^{2}, VMO)$ coefficients

Author(s): Hongjie Dong; N. V. Krylov
Journal: Trans. Amer. Math. Soc. 362 (2010), 6477-6494.
MSC (2000): Primary 35K10, 35K20, 35J15
Posted: August 3, 2010
MathSciNet review: 2678983
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Abstract: The solvability in Sobolev spaces $W^{1,2}_p$ is proved for nondivergence form second-order parabolic equations for close to 2. The leading coefficients are assumed to be measurable in the time variable and two coordinates of space variables, and almost VMO (vanishing mean oscillation) with respect to the other coordinates. This implies the $W^{2}_p$ -solvability for the same of nondivergence form elliptic equations with leading coefficients measurable in two coordinates and VMO in the others. Under slightly different assumptions, we also obtain the solvability results when .

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