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Calderón–Zygmund Estimate for Homogenization of Steady State Stokes Systems in Nonsmooth Domains

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Abstract

This paper investigates the higher integrability in homogenization theory for a generalized steady state Stokes system in divergence form with discontinuous coefficients in a bounded nonsmooth domain. We obtain a global and uniform Calderón–Zygmund estimate by essentially proving that both the gradient of the weak solution and its associated pressure are as integrable as the nonhomogeneous term under BMO smallness of the rapidly oscillating periodic coefficients and sufficient flatness of the boundary in the Reifenberg sense. The result improves previous works either concerned with nonhomogenization problem or focused on weakening the regularity requirements on both the coefficients and the boundary to the homogenization of such Stokes systems.

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Authors and Affiliations

  1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, 08826, Korea

    Sun-Sig Byun

  2. Center for Mathematical Analysis and Computations (CMAC), Yonsei University, Seoul, 03722, Korea

    Yunsoo Jang

  3. Department of Mathematical Sciences, Seoul National University, Seoul, 08826, Korea

    Hyoungsuk So

Authors
  1. Sun-Sig Byun
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  2. Yunsoo Jang
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  3. Hyoungsuk So
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Corresponding author

Correspondence to Yunsoo Jang.

Additional information

S. Byun was supported by NRF Grant (No. NRF-2015R1A4A1041675). Y. Jang was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (No. NRF-2016R1D1A1B03935364). H. So was supported by NRF Grant (No. NRF-2017R1A2B2003877).

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Byun, SS., Jang, Y. & So, H. Calderón–Zygmund Estimate for Homogenization of Steady State Stokes Systems in Nonsmooth Domains. J Dyn Diff Equat 30, 1945–1966 (2018). https://doi.org/10.1007/s10884-017-9638-7

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  • DOI: https://doi.org/10.1007/s10884-017-9638-7

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