Monotonicity, Gibbons' conjecture and Liouville theorem for the nonlocal Monge-Ampere problem with the Marchaud time derivative

View Full Paper

Ask AI

Bookmark

Maximum principles establish the monotonicity of solutions in the nonlocal Monge-Ampère problem, enhancing theoretical understanding.
Key evidence shows that effective maximum principles can be applied to gain insights into Gibbons' conjecture and Liouville theorem.
Analysis of nonlocal Monge-Ampère equations utilizes a sliding method combining time derivatives and maximum principles.
Findings underscore the significance of antisymmetric functions in proving the Liouville theorem, suggesting fruitful directions for future research.

Authors

Discussion

No takes yet. Share an insight, caveat, or question.

Analysis reveals maximum principles for nonlocal parabolic equations, suggesting new insights into monotonicity and related conjectures.

Mengru et al. (2025) studied this question.

View Full Paper

Ask AI

Bookmark