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Abstract 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… Click to show full abstract
Abstract 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.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2021
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