TY - JOUR
T1 - Monge-Ampère Equation with Bounded Periodic Data
AU - Li , Yanyan
AU - Lu , Siyuan
JO - Analysis in Theory and Applications
VL - 2
SP - 128
EP - 147
PY - 2022
DA - 2022/07
SN - 38
DO - http://doi.org/10.4208/ata.OA-0022
UR - https://global-sci.org/intro/article_detail/ata/20796.html
KW - Monge-Ampère equation, Liouville theorem.
AB - <p style="text-align: justify;">We consider the Monge-Ampère equation det $(D^2u) = f$ in $\mathbb{R}^n,$ where $f$ is a
positive bounded periodic function. We prove that $u$ must be the sum of a quadratic
polynomial and a periodic function. For $f ≡ 1,$ this is the classic result by Jörgens, Calabi and Pogorelov. For $f ∈ C^α,$ this was proved by Caffarelli and the first named
author.</p>