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Interior $C^2$ estimate for Monge-Ampère equation in dimension two


Author: Jiakun Liu
Journal: Proc. Amer. Math. Soc. 149 (2021), 2479-2486
MSC (2020): Primary 35J96; Secondary 35J62
DOI: https://doi.org/10.1090/proc/15459
Published electronically: March 22, 2021
MathSciNet review: 4246799
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Abstract: We obtain a genuine local $C^2$ estimate for the Monge-Ampère equation in dimension two, by using the partial Legendre transform.


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Additional 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
Article copyright: © Copyright 2021 American Mathematical Society