Global existence of solution for Monge–Ampére equation with an external periodic force on 3-dimensional torus. (August 2020)

• Record Type: Journal Article
• Authors: Li, Liangchen; Zhao, Xin
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: Monge–Ampére equation -- Torus -- Global existence; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111852
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is devoted to construction of a non-convex global solution for Monge–Ampére equation with an external periodic force on 3-dimensional torus. More precisely, we show that this non-convex solution is a periodic solution, which is unique in a ball with radius 1.