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On the L p -Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients

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Abstract

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable only in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI, 02912, USA

    Hongjie Dong

  2. Department of Applied Mathematics, Kyung Hee University, 1, Seochun-dong, Gihung-gu, Yongin-si, Gyeonggi-do, 446-701, Korea

    Doyoon Kim

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  1. Hongjie Dong
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  2. Doyoon Kim
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Correspondence to Hongjie Dong.

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Communicated by V. Šverák

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Dong, H., Kim, D. On the L p -Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients. Arch Rational Mech Anal 199, 889–941 (2011). https://doi.org/10.1007/s00205-010-0345-3

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  • DOI: https://doi.org/10.1007/s00205-010-0345-3

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