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

By Shibing Chen, Jiakun Liu, Xu-jia Wang. Annals of Mathematics, 2018

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In this paper, we establish the global $C^{2,\alpha}$ and $W^{2,p}$ regularity for the Monge-Amp\`ere equation subject to a natural boundary condition arising in optimal transportation.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/919525ea18bc8497be784e9af4d55fc541136a9f