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

• 成果类型: Article
• 署名作者: Trudinger, Neil S.; Wang, Xu-Jia
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.167.993
• 发表日期: 2008
• 页码: 993-1028
• 关键词: convex potentials; dirichlet problem; hypersurfaces; interior; MAPS

摘要

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.