Mathematical Research Letters

Volume 24 (2017)

Number 2

Two-dimensional Monge–Ampère equations under incomplete Hölder assumptions

Pages: 481 – 502

DOI: http://dx.doi.org/10.4310/MRL.2017.v24.n2.a11

Author

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

Abstract

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.

Keywords

Monge–Ampère equation, anisotropic regularity, <i>a priori</i> estimates

2010 Mathematics Subject Classification

Primary 35J96. Secondary 35J60.

Full Text (PDF format)

Paper received on 15 June 2015.