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

  • * Corresponding author: Xinghong Pan

    * Corresponding author: Xinghong Pan

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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  • 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.

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


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