6 papers · 1 filter
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 B…
Sharp global Alexandrov estimates and entire solutions of Monge-Ampère equations
Tianling Jin, Xushan Tu, Jingang Xiong
This paper continues our work [19] on sharp Alexandrov estimates. We obtain a sharp global uniform distance estimate from a convex function to the class of unimodular convex quadra…
Extremal Alexandrov estimates: singularities, obstacles, and stability
Tianling Jin, Xushan Tu, Jingang Xiong
The classical Alexandrov estimate controls the oscillation of a convex function by the mass of its associated Monge-Ampère measure and yields, for two convex functions of vari…
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 \[ \det D^2 v = v^q Ï_{\{v>0\}}, \quad v \geq 0 \text{ convex} \] with , where w…
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 \[ \operatorname{det} D^2 v=g v^qÏ_{\{v>0\}}, \quad v \geq 0, \] where is a constant and is a bou…
Extinction profiles for the Sobolev critical fast diffusion equation in bounded domains. I. One bubble dynamics
Tianling Jin, Jingang Xiong
In this paper, we investigate the extinction behavior of nonnegative solutions to the Sobolev critical fast diffusion equation in bounded smooth domains with the Dirichlet zero bou…