tianlingjin

JIN, Tianling
金天靈

(PhD Rutgers)

Phone: (852) 2358 7417
Email: tianlingjin@ust.hk
Office: Room 3424
Home Page

Associate Professor / PG Programs Coordinator



Research Interests

Analysis, Partial differential equations, Differential geometry

Teaching

  • MATH6900B  Mathematics Seminar
  • MATH6900C  Mathematics Seminar
  • MATH6900D  Mathematics Seminar
  • MATH6912P  Reading Course: Degenerate Parabolic Equations
  • MATH6990  MPhil Thesis Research
  • MATH7990  Doctoral Thesis Research

Awards & Honors

  • Professor Tianling JIN was awarded the 2023 Hong Kong Mathematical Society Young Scholar Award   (2023)
  • National Excellent Young Scientists Fund 2021   (2021)

Selected Publications

  Article

  1. Hölder regularity for the linearized porous medium equation in bounded domains
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Analysis in Theory and Applications, v. 40, (2), June 2024, p. 111-171
    • Year: 2024

  2. Optimal regularity and fine asymptotics for the porous medium equation in bounded domains
    • Author(s): Jin, Tianling; Ros-Oton, Xavier; Xiong, Jingang
    • Source: Journal fur die Reine und Angewandte Mathematik, v. 2024, (809), April 2024, p. 269-300
    • Year: 2024

  3. Stability of the separable solutions for a nonlinear boundary diffusion problem
    • Author(s): Jin, Tianling; Xiong, Jingang; Yang, Xuzhou
    • Source: Journal de Mathématiques Pures et Appliquées, v. 183, March 2024, p. 1-43
    • Year: 2024

  4. Existence of Solutions to a Conformally Invariant Integral Equation Involving Poisson-Type Kernels
    • Author(s): Du, Xusheng; Jin, Tianling; Yang, Hui
    • Source: Journal of Geometric Analysis, v. 33, (9), June 2023, article number 286
    • Year: 2023

  5. Optimal Boundary Regularity for Fast Diffusion Equations in Bounded Domains
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: American Journal of Mathematics, v. 145, (1), February 2023, article number 878650, p. 151-219
    • Year: 2023

  6. Local estimates for conformal Q-curvature equations
    • Author(s): Jin, Tianling; Yang, Hui
    • Source: Journal of Functional Analysis, v. 285, (2), July 2023, article number 109940
    • Year: 2023

  7. Blow up limits of the fractional laplacian and their applications to the fractional nirenberg problem
    • Author(s): Du, Xusheng; Jin, Tianling; Xiong, Jingang; Yang, Hui
    • Source: Proceedings of the American Mathematical Society, v. 151, (11), November 2023, p. 4693-4701
    • Year: 2023

  8. Bubbling and extinction for some fast diffusion equations in bounded domains
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Transactions of the American Mathematical Society Series B, v. 10, September 2023, p. 1287-1332
    • Year: 2023

  9. Singular extinction profiles of solutions to some fast diffusion equations
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Journal of Functional Analysis, v. 283, (7), 1 October 2022, article number 109595
    • Year: 2022

  10. On a Rayleigh-Faber-Krahn inequality for the regional fractional Laplacian
    • Author(s): Jin, Tianling; Kriventsov, Dennis; Xiong, Jingang
    • Source: Annals of Applied Mathematics, v. 37, (3), August 2021, p. 363-393
    • Year: 2021

  11. Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Annales de l'Institut Henri Poincaré C, Analyse non linéaire, v. 38, (4), July-August 2021, p. 1167-1216
    • Year: 2021

  12. An existence theorem on the isoperimetric ratio over scalar-flat conformal classes
    • Author(s): Chen, Xuezhang; Jin, Tianling; Ruan, Yuping
    • Source: Journal of Differential Equations, v. 269, (5), August 2020, p. 4116-4136
    • Year: 2020

  13. Hölder Gradient Estimates for a Class of Singular or Degenerate Parabolic Equations
    • Author(s): Imbert, Cyril; Jin, Tianling; Silvestre, Luis
    • Source: Advances in Nonlinear Analysis, v. 8, (1), March 2019, p. 845-867
    • Year: 2019

  14. Potential singularity for a family of models of the axisymmetric incompressible flow
    • Author(s): Hou, Thomas Y.; Jin, Tianling; Liu, Pengfei
    • Source: Journal of Nonlinear Science, v. 28, (6), December 2018, p. 2217-2247
    • Year: 2018

  15. Schauder estimates for an integro-differential equation with applications to a nonlocal Burgers equation
    • Author(s): Imbert, Cyril; Jin, Tianling; Shvydkoy, Roman
    • Source: Annales de la Faculté des Sciences de Toulouse. Mathématiques Sér. 6, v. 27, (4), 2018, p. 667-677
    • Year: 2018

  16. Minimizers for the Fractional Sobolev Inequality on Domains
    • Author(s): Frank, Rupert L.; Jin, Tianling; Xiong, Jingang
    • Source: Calculus of Variations and Partial Differential Equations, v. 57, (2), April 2018, article number 43
    • Year: 2018

  17. Dini and Schauder Estimates for Nonlocal Fully Nonlinear Parabolic Equations With Drifts
    • Author(s): Dong, Hongjie; Jin, Tianling; Zhang, Hong
    • Source: Analysis and PDE, v. 11, (6), 2018, p. 1487-1534
    • Year: 2018

  18. On the isoperimetric quotient over scalar-flat conformal classes
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Communications in Partial Differential Equations, v. 43, (12), December 2018, p. 1737-1760
    • Year: 2018

  19. The Nirenberg Problem and its Generalizations: a Unified Approach
    • Author(s): Jin, Tianling; Li, Yanyan; Xiong, Jingang
    • Source: Mathematische Annalen, v. 369, (1-2), October 2017, p. 109-151
    • Year: 2017

  20. Hölder Gradient Estimates for Parabolic Homogeneous p-Laplacian Equations
    • Author(s): Jin, Tianling; Silvestre, Luis
    • Source: Journal des Mathematiques Pures et Appliquees, v. 108, (1), July 2017, p. 63-87
    • Year: 2017

  21. On Local Behavior of Singular Positive Solutions to Nonlocal Elliptic Equations
    • Author(s): Jin, Tianling; De Queiroz, Olivaine Santana; Sire, Yannick; Xiong, Jingang
    • Source: Calculus of Variations and Partial Differential Equations, v. 56, (1), February 2017, article number 9
    • Year: 2017

  22. Propagation in a non local reaction diffusion equation with spatial and genetic trait structure
    • Author(s): Berestycki, Henri; Jin, Tianling; Silvestre, Luis E.
    • Source: Nonlinearity, v. 29, (4), March 2016, p. 1434-1466
    • Year: 2016

  23. Schauder estimates for nonlocal fully nonlinear equations
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, v. 33, (5), September 2016, p. 1375-1407
    • Year: 2016

  24. Solutions of Some Monge–Ampère Equations with Isolated and Line Singularities
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Advances in Mathematics, v. 289, February 2016, p. 114-141
    • Year: 2016

  25. On a fractional Nirenberg problem, part II: Existence of solutions
    • Author(s): Jin, Tianling; Li, YanYan; Xiong, Jingang
    • Source: International Mathematics Research Notices, v. 2015, (6), 2015, p. 1555-1589
    • Year: 2015

  26. Schauder estimates for solutions of linear parabolic integro-differential equations
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Discrete and Continuous Dynamical Systems, v. 35, (12), December 2015, p. 5977-5998
    • Year: 2015

  27. A sharp Sobolev trace inequality involving the mean curvature on Riemannian manifolds
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Transactions of the American Mathematical Society, v. 367, (9), 2015, p. 6751-6770
    • Year: 2015

  28. Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three
    • Author(s): Jin, Tianling; Maalaoui, Ali; Martinazzi, Luca; Xiong, Jingang
    • Source: Calculus of Variations and Partial Differential Equations, v. 52, (3-4), March 2015, p. 469-488
    • Year: 2015

  29. A Liouville Theorem for Solutions of Degenerate Monge-Ampère Equations
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Communications in Partial Differential Equations, v. 39, (2), February 2014, p. 306-320
    • Year: 2014

  30. A Fractional Yamabe Flow and Some Applications
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Journal für die Reine und Angewandte Mathematik, v. 2014, (696), November 2014, p. 187-223
    • Year: 2014

  31. On a fractional Nirenberg problem, part I: Blow up analysis and compactness of solutions
    • Author(s): Jin, Tianling; Li, YanYan; Xiong, Jingang
    • Source: Journal of the European Mathematical Society, v. 16, (6), 2014, p. 1111-1171
    • Year: 2014

  32. Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities
    • Author(s): Caffarelli, Luis; Jin, Tianling; Sire, Yannick; Xiong, Jingang
    • Source: Archive for Rational Mechanics and Analysis, v. 213, (1), July 2014, p. 245-268
    • Year: 2014

  33. Sharp constants in weighted trace inequalities on Riemannian manifolds
    • Author(s): Jin, Tianling; Xiong, Jingang
    • Source: Calculus of Variations and Partial Differential Equations, v. 48, (3-4), November 2013, p. 555-585
    • Year: 2013

  34. Symmetry and nonexistence of positive solutions of elliptic equations and systems with Hardy terms
    • Author(s): Jin, Tianling
    • Source: Annales de l'Institut Henri Poincaré C, Analyse non linéaire, v, 28, (6), November-December 2011, p. 965-981
    • Year: 2011

  35. Pathological solutions to elliptic problems in divergence form with continuous coefficients
    • Author(s): Jin, Tianling; Maz'ya, Vladimir; Van schaftingen, Jean
    • Source: Comptes Rendus Mathematique, v. 347, (13-14), July 2009, p. 773-778
    • Year: 2009