277 citations · 658 across the 44 of their papers we have counts for
48 papers
Sharp Sobolev inequalities under first moment constraints
Rupert L. Frank, Tianling Jin, Hua-Yang Wang +1
Let and . We study sharp Sobolev inequalities on the round sphere for functions satisfying $\int_{\mathbb{S}^n}x|u|^{np/…
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 , , and , we show that nonn…
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…
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…
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…
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…
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…
On the sharp constants in the regional fractional Sobolev inequalities
Rupert L. Frank, Tianling Jin, Wei Wang
In this paper, we study the sharp constants in fractional Sobolev inequalities associated with the regional fractional Laplacian in domains.
Existence of solutions to a conformally invariant integral equation involving Poisson-type kernels
Xusheng Du, Tianling Jin, Hui Yang
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature…
Hölder regularity for the linearized porous medium equation in bounded domains
Tianling Jin, Jingang Xiong
In this paper, we systematically study weak solutions of a linear singular or degenerate parabolic equation in a mixed divergence form and nondivergence form, which arises from the…
Optimal regularity and fine asymptotics for the porous medium equation in bounded domains
Tianling Jin, Xavier Ros-Oton, Jingang Xiong
We prove the optimal global regularity of nonnegative solutions to the porous medium equation in smooth bounded domains with the zero Dirichlet boundary condition after certain wai…
Stability of the separable solutions for a nonlinear boundary diffusion problem
Tianling Jin, Jingang Xiong, Xuzhou Yang
In this paper, we study a nonlinear boundary diffusion equation of porous medium type arising from a boundary control problem. We give a complete and sharp characterization of the…
Regularity of solutions to the Dirichlet problem for fast diffusion equations
Tianling Jin, Jingang Xiong
We prove global Hölder gradient estimates for bounded positive weak solutions of fast diffusion equations in smooth bounded domains with the homogeneous Dirichlet boundary conditio…
Blow up limits of the fractional Laplacian and their applications to the fractional Nirenberg problem
Xusheng Du, Tianling Jin, Jingang Xiong +1
We show a convergence result of the fractional Laplacian for sequences of nonnegative functions without uniform boundedness near infinity. As an application, we construct a sequenc…
On a Rayleigh-Faber-Krahn inequality for the regional fractional Laplacian
Tianling Jin, Dennis Kriventsov, Jingang Xiong
We study a Rayleigh-Faber-Krahn inequality for regional fractional Laplacian operators. In particular, we show that there exists a compactly supported nonnegative Sobolev function…
Local estimates for conformal -curvature equations
Tianling Jin, Hui Yang
We derive local estimates of positive solutions to the conformal -curvature equation near their singular set…
Singular extinction profiles of solutions to some fast diffusion equations
Tianling Jin, Jingang Xiong
We study extinction profiles of solutions to fast diffusion equations with some initial data in the Marcinkiewicz space. The extinction profiles will be the singular solutions of t…
Bubbling and extinction for some fast diffusion equations in bounded domains
Tianling Jin, Jingang Xiong
We study a Sobolev critical fast diffusion equation in bounded domains with the Brezis-Nirenberg effect. We obtain extinction profiles of its positive solutions, and show that the…
An existence theorem on the isoperimetric ratio over scalar-flat conformal classes
Xuezhang Chen, Tianling Jin, Yuping Ruan
Let be a smooth compact Riemannian manifold of dimension with smooth boundary , admitting a scalar-flat conformal metric. We prove that the supremum of the…