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Schauder estimates for higher-order parabolic systems with time irregular coefficients

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Abstract

We prove Schauder estimates for solutions to both divergence and non-divergence type higher-order parabolic systems in the whole space and a half space. We also provide an existence result for the divergence type systems in a cylindrical domain. All coefficients are assumed to be only measurable in the time variable and Hölder continuous in the spatial variables.

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Authors and Affiliations

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

    Hongjie Dong & Hong Zhang

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  1. Hongjie Dong
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  2. Hong Zhang
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Correspondence to Hongjie Dong.

Additional information

Communicated by N. Trudinger.

H. Dong and H. Zhang were partially supported by the NSF under agreement DMS-1056737.

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Dong, H., Zhang, H. Schauder estimates for higher-order parabolic systems with time irregular coefficients. Calc. Var. 54, 47–74 (2015). https://doi.org/10.1007/s00526-014-0777-y

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  • DOI: https://doi.org/10.1007/s00526-014-0777-y

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