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A note on the Harnack inequality for elliptic equations in divergence form


Authors: Dongsheng Li and Kai Zhang
Journal: Proc. Amer. Math. Soc. 145 (2017), 135-137
MSC (2010): Primary 35J15, 35B65; Secondary 35D30
DOI: https://doi.org/10.1090/proc/13174
Published electronically: June 10, 2016
MathSciNet review: 3565366
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Abstract: In 1957, De Giorgi proved the Hölder continuity for elliptic equations in divergence form and Moser gave a new proof in 1960. In the next year, Moser obtained the Harnack inequality. In this note, we point out that the Harnack inequality was hidden in De Giorgi's work.


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Additional Information

Dongsheng Li
Affiliation: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
Email: lidsh@mail.xjtu.edu.cn

Kai Zhang
Affiliation: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
Email: zkzkzk@stu.xjtu.edu.cn

DOI: https://doi.org/10.1090/proc/13174
Keywords: Elliptic equations, Harnack inequality
Received by editor(s): December 14, 2015
Received by editor(s) in revised form: February 28, 2016
Published electronically: June 10, 2016
Additional Notes: This research was supported by NSFC 11171266.
Communicated by: Joachim Krieger
Article copyright: © Copyright 2016 American Mathematical Society