Skip to main content
placeholder image

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

Journal Article


Abstract


  • In this paper, we establish the global C2,α and W2,p regularity for the Monge-Ampère equation detD2u= f subject to boundary condition Du(Ω)= Ω*, where Ω and Ω* are bounded convex domains in the Euclidean space Rn with C1,1 boundaries, and f is a Hölder continuous function. This boundary value problem arises naturally in optimal transportation and many other applications

Publication Date


  • 2021

Citation


  • Chen, S., Liu, J., & Wang, X. J. (2021). Global regularity for the Monge-Ampère equation with natural boundary condition. Annals of Mathematics, 194(3), 745-793. doi:10.4007/annals.2021.194.3.4

Scopus Eid


  • 2-s2.0-85129896819

Start Page


  • 745

End Page


  • 793

Volume


  • 194

Issue


  • 3

Abstract


  • In this paper, we establish the global C2,α and W2,p regularity for the Monge-Ampère equation detD2u= f subject to boundary condition Du(Ω)= Ω*, where Ω and Ω* are bounded convex domains in the Euclidean space Rn with C1,1 boundaries, and f is a Hölder continuous function. This boundary value problem arises naturally in optimal transportation and many other applications

Publication Date


  • 2021

Citation


  • Chen, S., Liu, J., & Wang, X. J. (2021). Global regularity for the Monge-Ampère equation with natural boundary condition. Annals of Mathematics, 194(3), 745-793. doi:10.4007/annals.2021.194.3.4

Scopus Eid


  • 2-s2.0-85129896819

Start Page


  • 745

End Page


  • 793

Volume


  • 194

Issue


  • 3