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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)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Interior $C^2$ estimate for Monge-Ampère equation in dimension two
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by Jiakun Liu
Proc. Amer. Math. Soc. 149 (2021), 2479-2486
DOI: https://doi.org/10.1090/proc/15459
Published electronically: March 22, 2021

Abstract:

We obtain a genuine local $C^2$ estimate for the Monge-Ampère equation in dimension two, by using the partial Legendre transform.
References
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Bibliographic Information
  • Jiakun Liu
  • Affiliation: School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales 2522, Australia
  • MR Author ID: 862211
  • ORCID: 0000-0003-4409-4187
  • Email: jiakunl@uow.edu.au
  • Received by editor(s): July 27, 2020
  • Published electronically: March 22, 2021
  • Additional Notes: This work was partially supported by the Australian Research Council DP170100929 and DP200101084.
  • Communicated by: Ryan Hynd
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 2479-2486
  • MSC (2020): Primary 35J96; Secondary 35J62
  • DOI: https://doi.org/10.1090/proc/15459
  • MathSciNet review: 4246799