Methods and Applications of Analysis

Volume 28 (2021)

Number 3

Special issue dedicated to Professor Ling Hsiao on the occasion of her 80th birthday, Part II

Guest editors: Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing), Hailiang Li (Capital Normal University, Beijing), Tao Luo (City University of Hong Kong), and Zhouping Xin (Chinese University of Hong Kong)

On a class of degenerate and singular Monge–Ampère equations

Pages: 371 – 386



Huaiyu Jian (Department of Mathematical Sciences, Tsinghua University, China)

You Li (School of Mathematics and Statistics, Beijing Technology and Business University, China)

Xushan Tu (Department of Mathematical Sciences, Tsinghua University, China)


In this paper we shall prove the existence, uniqueness and global Hölder continuity for the Dirichlet problem of a class of Monge–Ampère type equations which may be degenerate and singular on the boundary of convex domains. We will establish a relation of the Hölder exponent for the solutions with the convexity for the domains.


existence, uniqueness, global regularity, degenerate, singular, Monge–Ampère equation

2010 Mathematics Subject Classification

35J60, 35J96, 53A15

The authors’ work was supported by the NSFC (No. 12141103 and 12071017).

Received 16 April 2020

Accepted 28 May 2020

Published 10 June 2022