Maximum principles and Liouville results for uniformly elliptic nonlocal Bellman System. (January 2023)

• Record Type: Journal Article
• Authors: Peng, Shaolong
• Is Part Of: Nonlinear analysis. Volume 226(2023)
• Publication Date: 2023-01
• Subjects: primary 35R11 62F30 -- secondary 35B06 35B53; Bellman system -- Maximum principles -- Method of moving planes -- Monotonicity -- Symmetry -- Liouville-type results; 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.2022.113141
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we are concerned with the uniformly elliptic nonlocal Bellman system. Firstly, we study different maximum principles for the uniformly elliptic nonlocal Bellman operators and obtain key ingredients for carrying on the method of moving planes. Then we derive qualitative properties of solutions to the uniformly elliptic nonlocal Bellman in bounded domains, unbounded domains, and a coercive epigraph domain Ω in R n, respectively, such as monotonicity, symmetry, and Liouville-type results.