Monge-Ampère Equation with Bounded Periodic Data (Analysis in Theory and Applications, 2022)
We consider the Monge-Ampère equation det $(D^2u) = f$ in $\mathbb{R}^n,$ where $f$ is apositive bounded periodic function. We prove that $u$ must be the sum of a quadraticpolynomial 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 namedauthor.