Abstract
In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Ampère equation when the inhomogeneous term is only assumed to be Hölder continuous. As a consequence of our approach, we also establish the existence and uniqueness of globally smooth solutions to the second boundary value problem for the affine maximal surface equation and affine mean curvature equation.
Original language | English |
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Pages (from-to) | 993-1028 |
Number of pages | 36 |
Journal | Annals of Mathematics |
Volume | 167 |
Issue number | 3 |
DOIs | |
Publication status | Published - May 2008 |