On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients

Hongjie Dong; Xinghong Pan

doi:10.3934/dcds.2021049

Article Contents

2021, Volume 41, Issue 10: 4567-4592. Doi: 10.3934/dcds.2021049

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On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients

Hongjie Dong^1, and
Xinghong Pan^2, ,

1.
Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA
2.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

^* Corresponding author: Xinghong Pan
^* Corresponding author: Xinghong Pan

Received: September 30, 2020

Revised: January 31, 2021

Early access: March 2021

Published: October 2021

H. Dong was partially supported by the Simons Foundation, grant # 709545. X. Pan is supported by Natural Science Foundation of Jiangsu Province (No. BK20180414) and National Natural Science Foundation of China (No. 11801268)

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Abstract

We show that weak solutions to parabolic equations in divergence form with conormal boundary conditions are continuously differentiable up to the boundary when the leading coefficients have Dini mean oscillation and the lower order coefficients verify certain integrability conditions.

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Mathematics Subject Classification: Primary: 35K20, 35B45; Secondary: 35B65.

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References

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