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 Rn, respectively, such as monotonicity, symmetry, and Liouville-type results.
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