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math.AP2025
A Liouville theorem for convex functions with periodic Monge-Ampère measure
Tianling Jin, YanYan Li, Hung V. Tran +1
We study global convex solutions of the Monge-Ampère equation \[ \det D^2 u = μ\quad \text{in } \mathbb{R}^n, \] where is a nonnegative locally finite periodic Bore…
math.AP2025
On the singular set of the free boundary for a Monge-Ampère obstacle problem
Tianling Jin, Xushan Tu, Jingang Xiong
This is a continuation of our earlier work [14] on the Monge-Ampère obstacle problem \[ \det D^2 v = v^q χ_{\{v>0\}}, \quad v \geq 0 \text{ convex} \] with , where we…
math.AP2025
Regularity and classification of the free boundary for a Monge-Ampère obstacle problem
Tianling Jin, Xushan Tu, Jingang Xiong
We study convex solutions to the Monge-Ampère obstacle problem \[ \operatorname{det} D^2 v=g v^qχ_{\{v>0\}}, \quad v \geq 0, \] where is a constant and is a bound…