The sliding method for the nonlocal Monge–Ampère operator. (July 2020)

• Record Type: Journal Article
• Authors: Chen, Xueying; Bao, Gejun; Li, Guanfeng
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: A sliding method -- The nonlocal Monge–Ampère operator -- Narrow region principle -- Monotonicity -- Bounded domains -- The whole space; 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.2020.111786
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We develop a sliding method for the nonlocal Monge–Ampère operator. We first establish a narrow region principle in bounded domains, which plays an important role in the sliding method. Then we consider the equation with the nonlocal Monge–Ampère operator and derive the monotonicity of solutions in both bounded domains and the whole space. We use a new idea-estimating the singular integrals defining the nonlocal Monge–Ampère operator along a sequence of approximate maximum points.