Mathematical Research Letters

Volume 24 (2017)

Number 2

Two-dimensional Monge–Ampère equations under incomplete Hölder assumptions

Pages: 481 – 502



Qi-Rui Li (Centre for Mathematics and Its Applications, Australian National University, Canberra, ACT, Australia)


In this paper, we study the regularity of solutions of the Monge–Ampère equation in two dimensions when the inhomogeneous term is Hölder continuous only in one variable or piecewise Hölder continuous.


Monge–Ampère equation, anisotropic regularity, a priori estimates

2010 Mathematics Subject Classification

Primary 35J96. Secondary 35J60.

Received 15 June 2015

Published 24 July 2017