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Orlicz regularity for higher order parabolic equations in divergence form with coefficients in weak BMO

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Abstract

We consider higher order parabolic equations in divergence form with measurable coefficients to find optimal regularity in Orlicz spaces of the maximum order derivatives of the weak solutions. The relevant minimal regularity requirement on the tensor matrix coefficients is of small BMO in the spatial variable and is measurable in the time variable. As a consequence we prove the classical W m,p regularity, m = 1, 2, . . . , 1 < p < ∞, for such higher order equations. In the same spirit the results easily extend to higher order parabolic systems as well as up to the boundary.

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Authors and Affiliations

  1. Department of Mathematics and Research Institute of Mathematics, Seoul National University, Seoul, 151-747, Korea

    Sun-Sig Byun & Seungjin Ryu

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  1. Sun-Sig Byun
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  2. Seungjin Ryu
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Correspondence to Sun-Sig Byun.

Additional information

This work was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST)(2009-0093135).

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Byun, SS., Ryu, S. Orlicz regularity for higher order parabolic equations in divergence form with coefficients in weak BMO. Arch. Math. 95, 179–190 (2010). https://doi.org/10.1007/s00013-010-0151-z

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