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

By Neil S. Trudinger, Xu-jia Wang. 2005

174 citations recorded by the source corpus.

In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Ampere equation when the inhomoge- neous 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d839b0d82c7115f568fc9998e043b271e4266a24

How researchers see this paper

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In Applied Mathematics

1. Monika Ludwig
2. Yu Wang
3. J. Bao
4. Yanyan Li
5. Xu-jia Wang
6. Haigang Li
7. Lei Zhang
8. Yiming Zhao

In Geometry and Topology

1. Yu Wang
2. Monika Ludwig
3. J. Bao
4. Xu-jia Wang
5. Haigang Li
6. Lei Zhang
7. Franz E. Schuster
8. Robert J. McCann

Citations in the corpus

• General affine surface areas (2009, background): “Numerous important results regarding equi-affine surface area were obtained in recent years (see, for example, [1], [2], [40], [43] – [46]).”
• On the $C^{2,α}$-regularity of the complex Monge–Ampère equation (2012, methodology): “Sharp boundary estimates were subsequently obtained by Trudinger and Wang [15].”
• Monge–Ampère equation on exterior domains (2013, background): “J. Bao (B) · H. Li Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Ministry of Education, Beijing 100875, China e-mail: jgbao@bnu.edu.cn H. Li e-mail: hgli@bnu.edu.cn L. Zhang Department of Mathematics, University of Florida, 358 Little Hall”
• The k-Hessian Equation (2009, background): “The boundary C2;fi estimate for the Dirichlet problem was established in [ TW6 ], assuming that f > 0;2 Cfi(›), the boundary @› is uniformly convex and C3 smooth, and boundary function ’ 2 C3. If either @› or ’ is”