Abstract
We investigate the unique solvability of second order parabolic equations in non-divergence form in \(W_p^{1,2}((0,T) \times \mathbb{R}^d)\), p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.
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The second author was partially supported by NSF Grant DMS-0140405.
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Kim, D., Krylov, N.V. Parabolic Equations with Measurable Coefficients. Potential Anal 26, 345–361 (2007). https://doi.org/10.1007/s11118-007-9042-8
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DOI: https://doi.org/10.1007/s11118-007-9042-8