Abstract
We establish \(L_{q,p}\)-estimates and solvability for mixed Dirichlet–conormal problems for parabolic equations in a cylindrical Reifenberg-flat domain with a rough time-dependent separation.
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The authors would like to thank the anonymous referee for careful reading of the manuscript and helpful comments.
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Communicated by L. Szekelyhidi.
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J. Choi was partially supported by the National Research Foundation of Korea (NRF) under agreements NRF-2019R1F1A1058826 and NRF-2022R1F1A1074461 H. Dong was partially supported by the Simons Foundation, Grant No. 709545, a Simons fellowship, Grant No. 007638, and the NSF under agreement DMS-2055244. Z. Li was partially supported by an AMS-Simons travel grant.
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Choi, J., Dong, H. & Li, Z. Mixed boundary value problems for parabolic equations in Sobolev spaces with mixed-norms. Calc. Var. 62, 5 (2023). https://doi.org/10.1007/s00526-022-02327-z
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DOI: https://doi.org/10.1007/s00526-022-02327-z