Boundary C^{2,\alpha} estimates for Monge-Ampere type equations

Authors

Yong Huang, Hunan UniversityFollow
Feida Jiang, Tsinghua UniversityFollow
Jiakun Liu, University of WollongongFollow

RIS ID

101313

Publication Details

Huang, Y., Jiang, F. & Liu, J. (2015). Boundary C2,α estimates for Monge–Ampère type equations. Advances in Mathematics, 281 706-733.

Abstract

In this paper, we obtain global second derivative estimates for solutions of the Dirichlet problem of certain Monge-Ampère type equations under some structural conditions, while the inhomogeneous term is only assumed to be Hölder continuous and bounded away from zero and infinity. These estimates correspond to those for the standard Monge-Ampère equation obtained by Trudinger and Wang (2008) and by Savin (2013), and have natural applications in optimal transportation and prescribed Jacobian equations.

Grant Number

ARC/DE140101366

Additional Grant Number

http://purl.org/au-research/grants/arc/DE140101366