Year: 2022
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 2 : pp. 128–147
Abstract
We consider the Monge-Ampère equation det (D2u)=f in Rn, 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∈Cα, this was proved by Caffarelli and the first named author.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-0022
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 2 : pp. 128–147
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Monge-Ampère equation Liouville theorem.