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Global regularity for the Monge-Ampère equation with natural boundary condition

Shibing Chen School of Mathematical Sciences, University of Science and Technology of China, Hefei, P.R. China Jiakun Liu School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, Australia Xu-Jia Wang Centre for Mathematics and Its Applications, The Australian National University, Canberra, Australia

Analysis of PDEs mathscidoc:2203.03009

Annals of Mathematics, 194, 745-793, 2021.11
In this paper, we establish the global C^{2,α} and W^{2,p} regularity for the Monge-Amp`ere equation det D^2u = f subject to boundary condition Du(Ω) = Ω^∗, where Ω and Ω^∗ are bounded convex domains in the Euclidean space R^n with C^{1,1} boundaries, and f is a Ho ̈lder continuous function. This boundary value problem arises naturally in optimal transportation and many other applications.
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@inproceedings{shibing2021global,
  title={Global regularity for the Monge-Ampère equation with natural boundary condition},
  author={Shibing Chen, Jiakun Liu, and Xu-Jia Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220316114824102546984},
  booktitle={Annals of Mathematics},
  volume={194},
  pages={745-793},
  year={2021},
}
Shibing Chen, Jiakun Liu, and Xu-Jia Wang. Global regularity for the Monge-Ampère equation with natural boundary condition. 2021. Vol. 194. In Annals of Mathematics. pp.745-793. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220316114824102546984.
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