Global regularity for the Monge-Ampère equation with natural boundary condition
Publication Name
Annals of Mathematics
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
Open Access Status
This publication may be available as open access
Volume
194
Issue
3
First Page
745
Last Page
793
Funding Number
DP170100929
Funding Sponsor
Australian Research Council