1 citations · 1 across the 12 of their papers we have counts for
13 papers
Quantitative homogenization of Monge-Ampère equations in periodic media
Tianling Jin, YanYan Li, Hung V. Tran +1
Let and be the convex solutions of \[ \det D^2u^\varepsilon=F(x,x/\varepsilon),\qquad \det D^2u=\overline F(x) \] on a bounded convex domain , with the same…
Optimal regularity and fine asymptotics for very fast diffusion equations in bounded domains
Tianling Jin, Xushan Tu, Jingang Xiong +1
We prove the optimal global regularity of admissible solutions to a transformed very fast diffusion equation in the range , posed on smooth bounded domains with zero Dirich…
Schauder estimates for the linearized very fast diffusion equations in bounded domains
Tianling Jin, Xushan Tu, Jingang Xiong +1
We establish Schauder estimates for linearized very fast diffusion equations with Dirichlet boundary conditions in bounded smooth domains. These estimates provide an important ingr…
Regularity for convex viscosity solutions of Equation
Ruosi Chen, Huaiyu Jian, Xushan Tu +1
We prove interior regularity result for convex viscosity solutions of the quadratic Hessian equation , under the assumption that with $\inf…
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 varia…
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…
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…
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…
Strong maximum principle for generalized solutions to equations of the Monge-Ampère type
Huaiyu Jian, Xushan Tu
In this paper, we investigate the strong maximum principle for generalized solutions of Monge-Ampère type equations. We prove that the strong maximum principle holds at points wher…
Boundary Regularity for the Oblique Boundary Value Problem of Monge-Ampère Equations
Huaiyu Jian, Xushan Tu
We study the good shape property of boundary sections of convex solutions of the oblique boundary value problem for Monge-Ampère equations $$\det D^2u =f(x) \text{ in } Ω, \quad D_…
A Liouville theorem for the Neumann problem of the Monge-Ampere equation
Huaiyu Jian, Xushan Tu
In this paper, we study the Neumann problem of Monge-Ampère equations in Semi-space. For two dimensional case, we prove that its viscosity convex solutions must be a quadratic poly…
On A Class of Degenerate And Singular Monge-Ampère Equations
Huaiyu Jian, You Li, Xushan Tu
In this paper we shall prove the existence, uniqueness and global Hlder continuity for the Dirichlet problem of a class of Monge-Ampère type equations which may be degene…