A note on the Harnack inequality for elliptic equations in divergence form
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- by Dongsheng Li and Kai Zhang PDF
- Proc. Amer. Math. Soc. 145 (2017), 135-137 Request permission
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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Additional 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