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J. Korean Math. Soc. 2020; 57(6): 1509-1533

Online first article July 21, 2020      Printed November 1, 2020

https://doi.org/10.4134/JKMS.j190777

Copyright © The Korean Mathematical Society.

Gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients

Jongkeun Choi, Seick Kim, Kyungrok Lee

Pusan National University; Yonsei University; Yonsei University

Abstract

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We provide detailed proofs for local gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients in a ball and a half ball.

Keywords: Elliptic equation, measurable coefficients, partial Dini mean oscillation condition, $W^{1,\infty}$-estimate, weak type-$(1,1)$ estimate

MSC numbers: 35B65, 35J47, 35R05

Supported by: J. Choi is partially supported by National Research Foundation of Korea(NRF) under agreement NRF-2019R1F1A1058826 S. Kim is partially supported by National Research Foundation of Korea(NRF) under agreement NRF-20151009350 and NRF-2019R1A2C2002724

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