Boundary regularity for the Monge-Ampere and affine maximal surface equations

Details Boundary regularity for the Monge-Ampere and affine maximal surface equations Boundary regularity for the Monge-Ampere and affine maximal surface equations

2005-09-15

arxiv.org/abs/math/0509342v1

Mathematics

Differential Geometry

38

Scientific paper

In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Ampere equation when the inhomogeneous term is only assumed to be Holder 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.

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