Monotonicity of solutions for the uniformly elliptic nonlocal Bellman equation on the upper half space

作者：Chen, Xueying; Bao, Gejun; Li, Guanfeng^*

来源：Journal of Mathematical Analysis and Applications, 2021, 496(2): 124843.

DOI：10.1016/j.jmaa.2020.124843

• Sliding method
• Uniformly elliptic nonlocal Bellman operator
• Maximum principle
• Upper half space
• Monotonicity
• Uniqueness

In this paper, we develop a sliding method for the uniformly elliptic nonlocal Bellman operator. We first establish a maximum principle on an upper half space, which plays an important role in the sliding method. Then we consider equations involving the uniformly elliptic nonlocal Bellman operator on the upper half space, and prove the monotonicity and uniqueness of solutions for the uniformly elliptic nonlocal Bellman equation. We use a new idea-estimating the singular integrals defining the operator along a sequence of approximate maximum points.

• 单位
  harbin inst technol