Tianling Jin

activity

20092026

most citedOn a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions

277 citations · 658 across the 44 of their papers we have counts for

collaborators

Showing 2026Show all

8 papers · 1 filter

math.AP2026

Sharp Sobolev inequalities under first moment constraints

Rupert L. Frank, Tianling Jin, Hua-Yang Wang +1

Let $n \geq 2$ and $1 < p < n$ . We study sharp Sobolev inequalities on the round sphere $S^{n}$ for functions $u \in W^{1, p} (S^{n})$ satisfying $\int_{\mathbb{S}^n}x|u|^{np/…

math.AP2026

Boundary regularity for fractional porous medium-type equations in bounded domains

Mengyu Huo, Tianling Jin, Jingang Xiong

We prove boundary Hölder regularity for fractional porous medium-type equations in bounded smooth domains with zero exterior data. For $0 < σ < 1$ , $n > 2 σ$ , and $m > 1$ , we show that nonn…

math.AP2026

Quantitative homogenization of Monge-Ampère equations in periodic media

Tianling Jin, YanYan Li, Hung V. Tran +1

Let $u^{ε}$ and $u$ 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 $Ω$ , with the same…

math.AP2026

Łojasiewicz--Simon inequalities near bubbling configurations for the Yamabe functional on bounded domains

Tianling Jin, Jingang Xiong, Ning Zhou

We establish Łojasiewicz--Simon type gradient inequalities for the Yamabe functional on bounded smooth domains near configurations consisting of finitely many concentrating bubbles…

math.AP2026

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 $- 1 < p < 0$ , posed on smooth bounded domains with zero Dirich…

math.AP2026

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…

math.AP2026

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…

math.AP2026

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 $n$ varia…