Monotonicity of solutions for a class of uniformly elliptic nonlocal Bellman systems
Guanfeng Li, Xueying Chen · Complex Variables and Elliptic Equations · 2021
This paper is concerned with a class of uniformly elliptic nonlocal Bellman systems in unbounded Lipschitz domains. There are two major ingredients. The first is a narrow region principle in unbounded domains. We can use this to carry out the direct method of moving planes. The second ingredient is to prove the monotonicity of positive bounded solutions for a cooperative system with uniformly elliptic nonlocal Bellman operators. Without decay assumptions on solutions, we estimate the singular integrals defining the operator along a sequence of approximate minimum points.