Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A note on the Harnack inequality for elliptic equations in divergence form
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by Dongsheng Li and Kai Zhang
Proc. Amer. Math. Soc. 145 (2017), 135-137
DOI: https://doi.org/10.1090/proc/13174
Published electronically: June 10, 2016

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.
References
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Bibliographic Information
  • Dongsheng Li
  • Affiliation: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
  • MR Author ID: 647543
  • 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
  • MR Author ID: 1098004
  • Email: zkzkzk@stu.xjtu.edu.cn
  • 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
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 135-137
  • MSC (2010): Primary 35J15, 35B65; Secondary 35D30
  • DOI: https://doi.org/10.1090/proc/13174
  • MathSciNet review: 3565366