中文 Tsinghua University Access to the old version Talent Recruitment

Hu Jiaxin

  • Professor
  • Tel: +86 10 627-87513
  • Email: hujiaxin@tsinghua.edu.cn

Education

PhD (2001), University of St-Andrews, UK.


Work Experience

2007- Present, Full Professor at Department of Mathematical Sciences, Tsinghua University, Beijing, China


Research Interests

l Partial Differential Equation

l Fractal Geometry

l Heat kernel and Dirichlet form

l Stochastic process


Teaching

Undergraduate courses:

l Calculus .

l Linear Algebra and Geometry.

l Multi-Variable Calculus.

l Probability theory and Statistics

Graduate courses

l Complex Analysis

l Fractal Geometry,

l Geometric measure theory.

l Harmonic Analysis.


Selected Publications

  1. A. Grigor'yan, E. Hu, and J. Hu, Tail estimates and off-diagonal upper bounds of the heat kernel, preprint, 2024.

  2. J. Hu and Z. Yu,  Strong elliptic Harnack inequality and heat kernel estimate for the resurrected Dirichlet form, preprint, 2024.

  3. A. Grigor'yan, Eryan Hu and Jiaxin Hu, Parabolic mean value inequality and on-diagonal upper bound of the heat kernel on doubling spaces, Math. Ann. 389 (2024), pp. 24112467.

  4. A. Grigor'yan, E. Hu, and J. Hu, Mean value inequality and generalized capacity on doubling spaces, Pure Appl. Funct. Anal., 9 (2024), pp. 111168.

  5. Kenneth J. Falconer and Jiaxin Hu and Junda, Zhang. A dichotomy on the self-similarity of graph-directed attractors, Journal of Fractal Geometry 11 (2024). 161204.

  6. Jiaxin Hu and Zhenyu Yu. The weak eliptic Harnack inequality revisited, Asian J. Math, Special Issue in memory of Professor Ka-Sing Lau, 27 (2023), pp. 771828.

  7. A. Grigor'yan, Eryan Hu and Jiaxin Hu, Off-diagonal lower estimates and Hölder regularity of the heat kernel, Special Issue in memory of Professor Ka-Sing Lau, 27 (2023), pp. 675771.

  8. Jiaxin Hu and Guanhua Liu. "Upper estimates of heat kernels for non-local Dirichlet forms on doubling spacesForum Mathematicum, vol. 34, no. 1, 2022, pp. 225-277.

  9. A. Bendikov, A. Grigor'yan, Eryan Hu and Jiaxin Hu, Heat kernels and non-local Dirichlet forms on ultrametric spaces, Annali della Scuola Normale Superiore di Pisa- Classe di ScienzeVol. XXII (2021), 399-461.

  10. A. Grigor'yanEryan Hu and Jiaxin HuTwo-sided estimates of heat kernels of jump type Dirichlet forms, Adv. Math. 330 (2018), 433-515.

  11. A. Grigor'yanEryan Hu and Jiaxin HuLower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces, J. Funct. Anal. 272 (2017), 33113346.

  12. A. Grigor'yanJiaxin Hu and Ka-Sing LauGeneralized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces, J. Math. Soc. Japan, 67 (2015), 1485-1549.

  13. A. Grigor'yanJiaxin Hu and Ka-Sing LauEstimates of heat kernels for non-local regular Dirichlet forms, Trans. Amer. Math. Soc. 366 (2014), 6397-6441.

  14. A. Grigor'yanJiaxin Hu, Upper bounds of heat kernels on doubling spaces, Moscow Math. J. 14 (2014), No. 3, 505-563.

  15. A. Grigor'yanJiaxin Hu, Heat kernels and Green functions on metric measure spaces, Canadian J. Math. 66 (2014),      641-699.

  16. A. Grigor'yan, J. Hu and K.-S. Lau, Comparison inequalities for heat semigroups and heat kernels on metric measure spaces, J. Funct. Anal. 259 (2010), 2613-2641.

  17. Jiaxin Hu and Martina Zähle: Generalized Bessel and Riesz potentials on metric measure spaces, Potential Anal. 30 (2009), 315-340.

  18. A. Grigoryan and Jiaxin Hu: Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric      spaces, Inventiones Mathematicae 174 (2008), 81-126.

  19. A. Grigoryan; Jiaxin Hu and Ka-Sing Lau: Obtaining upper bounds of heat kernels from lower bounds, Comm. Pure Appl. Math. 61 (2008), no. 5, 639-660.

  20. Jiaxin Hu and X.P. Huang, A note on the limiting weak-type behavior for maximal operators, Proc. Amer. Math. Soc. 136 (2008), 1599-1607.

  21. A. Grigoryan, Jiaxin Hu and Ka-Sing Lau: Equivalence conditions for on-diagonal upper bounds of heat kernels on      self-similar spaces, J. Funct. Anal. 237 (2006), 427-445.

  22. Jiaxin Hu, K.-S. Lau and S.-M. Ngai: Laplace operators related to self-similar measures on Rd, J. Funct. Anal. 239 (2006), 542-565.

  23. A. Grigoryan, Jiaxin Hu and Ka-Sing Lau: Heat kernels on metric-measure spaces and an application to semi-linear elliptic equations, Trans. Amer. Math. Soc. 355 (2003), 2065--2095.

  24. Kenneth J. Falconer and Jiaxin Hu: Nonlinear diffusion equations on unbounded fractal domains. J. Math. Anal. Appl. 256 (2001), 606624.

  25. Jiaxin Hu and P.G. LeFloch: L1-continuous dependence property for systems of conservation laws, Arch. Rational Mech. Anal. 151 (2000), 45-93.

  26. Jiaxin Hu: The Riemann problem for pressureless uid dynamics with distribution solutions in Colombeau’s sense, Comm. Math. Phys, 194 (1998), 191-205.

  • BookAn introduction to fractal analysis (in Chinese, 230 pages), Science Press, 2013.