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L p-regularity for fourth order parabolic systems with measurable coefficients

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Abstract

We treat fourth order parabolic systems in divergence form with bounded measurable coefficients. We establish Hessian estimates for such parabolic systems by proving that the L p-regularity of the inhomogeneous terms exactly reflects in the regularity of the Hessian of the solutions for every \({p \in (1, \infty)}\) . The assumptions are that the coefficients are allowed to be merely measurable in one of spatial variables, but averaged in the other spatial variables and time variable.

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Authors and Affiliations

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

    Sun-Sig Byun

  2. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Lihe Wang

  3. Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, China

    Lihe Wang

Authors
  1. Sun-Sig Byun
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  2. Lihe Wang
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Correspondence to Sun-Sig Byun.

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Byun, SS., Wang, L. L p-regularity for fourth order parabolic systems with measurable coefficients. Math. Z. 272, 515–530 (2012). https://doi.org/10.1007/s00209-011-0947-y

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  • DOI: https://doi.org/10.1007/s00209-011-0947-y

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