Symmetry of solutions for a class of nonlocal Monge–Ampère equations. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Chen, Xueying; Bao, Gejun; Li, Guanfeng
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 1(2022)
• Page Start: 129
• Page End: 150
• Publication Date: 2022-01-02
• Subjects: Nonlocal Monge–Ampère operators -- narrow region principle -- decay at infinity -- direct method of moving planes -- an ellipsoid region; 35B06 -- 35J60; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1816986
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: In this paper, we consider equations involving a class of nonlocal Monge–Ampère operators. We first establish some maximum principles, such as a narrow region principle and a decay at infinity. Then, by using the direct method of moving planes, we obtain the symmetry of solutions in an ellipsoid region and in the whole space. We also prove that the positive solutions are non-existence on the upper half space.