277 citations · 752 across the 50 of their papers we have counts for
53 papers
Classification and asymptotics for the boundary Yamabe equation with an isolated singularity
Tianling Jin, Yuxuan Liao, Jingang Xiong
We classify positive singular solutions of the boundary Yamabe equation on the punctured half-space in every dimension . Previous symmetry results reduce this problem to a n…
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…
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…
The Critical Semilinear Elliptic Equation with Isolated Boundary Singularities II
Hua-Yang Wang, Jingang Xiong
Continuing the work of the second author (2017), we study the Sobolev critical semilinear elliptic equation in the half-space with an isolated boundary singularity and zero Dirichl…
Existence of non-radial entire solutions for the Hénon equation beyond even exponents
Qinfeng Jiang, Jingang Xiong
This paper is concerned with the existence of non-radial positive classical solutions for the critical Hénon equation \[ -Δu=|x|^αu^{\frac{N+2+2α}{N-2}} \qquad \text{in }\mathbb R^…
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…
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…
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…
Asymptotic Analysis of Harmonic Maps With Prescribed Singularities
Qing Han, Marcus Khuri, Gilbert Weinstein +1
This is the first in a series of two papers to establish the mass-angular momentum inequality for multiple black holes. We study singular harmonic maps from domains of 3-dimensiona…
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 viscosity solutions of the -Loewner-Nirenberg problem
YanYan Li, Luc Nguyen, Jingang Xiong
We study the regularity of the viscosity solution of the -Loewner-Nirenberg problem on a bounded smooth domain for . It was known that $u…
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…
Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric
Zhengchao Han, Jingang Xiong, Lei Zhang
We prove that any positive solution of the Yamabe equation on an asymptotically flat -dimensional manifold of flatness order at least and must converge…
Sharp Sobolev inequalities involving boundary terms revisited
Zhongwei Tang, Jingang Xiong, Ning Zhou
We revisit the sharp Sobolev inequalities involving boundary terms on Riemannian manifolds with boundaries proved by \emph{[Y.Y. Li and M. Zhu, Geom. Funct. Anal. \textbf{8} (1998)…
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…