胡家信 - 清华大学 - 数学科学系

个人简介

清华大学数学科学系长聘教授、博士（英国圣安德鲁斯大学，2001）工作履历 2023.06-2023.08，德国比勒菲尔德（Bielefeld）大学数学系 2020.01-2020.02, 加拿大大不列颠哥伦比亚大学（UBC）访问教授 2019.01-2019.02，日本京都大学访问教授 2018.01-2018.02, 泰国兰实大学(Rangsit University)访问教授 2014.05-2014.06，美国康乃尔大学，访问教授 2008.01-2020.12，多次访问德国比勒菲尔德大学(Bielefeld)，合作研究 2007-现在，清华大学数学科学系，教授 2004.01-2020.12，多次访问香港中文大学数学系，合作研究 2003.03-2004.07，德国耶拿（Jena）大学，洪堡研究学者 2001.09-2002.08，香港中文大学，博士后及兼职老师 1997.11-1998.10，巴黎高等理工大学（Ecole Polytechnique），访问学者所授课程调和分析引论（研究生）概率论与数理统计（本科生）线性代数（本科生）微积分（本科生）几何测度论（研究生）分形几何（研究生）复分析（研究生）概率论（本科生）代数与几何（本科生）数学专题课（本科生）奖励与荣誉德国洪堡学者（2002-03至2003-07，德国耶拿大学）

研究领域

偏微分方程，分形几何，狄氏型理论、热核估计

近期论文

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A. Grigor'yan, Eryan Hu and Jiaxin Hu, Parabolic mean value inequality and on-diagonal upper bound of the heat kernel on doubling spaces, Mathematische Annalen (2023)， https://doi.org/10.1007/s00208-023-02699-3 A. Grigor'yan, Eryan Hu and Jiaxin Hu, Mean value inequality and generalized capacity on doubling spaces, to appear in J. Pure and Applied Funct. Anal. Falconer, Kenneth J. and Hu, Jiaxin and Zhang, Junda. A dichotomy on the self-similarity of graph-directed attractors, to appear in J. Fractal Geom. Hu, Jiaxin and Yu, Zhenyu. The weak elliptic Harnack inequality revisited, to appear in Asian J. Math, Special Issue in memory of Professor Ka-Sing Lau. Hu, Jiaxin and Liu, Guanhua. "Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces，Forum Mathematicum, vol. 34, no. 1, 2022, pp. 225-277. 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 Scienze，Vol. XXII (2021), 399-461. A. Grigor'yan，Eryan Hu and Jiaxin Hu，Two-sided estimates of heat kernels of jump type Dirichlet forms, Adv. Math. 330 (2018), 433-515. A. Grigor'yan，Eryan Hu and Jiaxin Hu，Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces, J. Funct. Anal. 272 (2017), 3311–3346. A. Grigor'yan，Jiaxin Hu and Ka-Sing Lau，Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces, J. Math. Soc. Japan, 67 (2015), 1485-1549. A. Grigor'yan，Jiaxin Hu and Ka-Sing Lau，Estimates of heat kernels for non-local regular Dirichlet forms, Trans. Amer. Math. Soc. 366 (2014), 6397-6441. A. Grigor'yan，Jiaxin Hu, Upper bounds of heat kernels on doubling spaces, Moscow Math. J. 14 (2014), No. 3, 505-563. A. Grigor'yan，Jiaxin Hu, Heat kernels and Green functions on metric measure spaces, Canadian J. Math. 66 (2014), 641-699. 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. Jiaxin Hu and Martina Z?hle: Generalized Bessel and Riesz potentials on metric measure spaces, Potential Anal. 30 (2009), 315-340. A. Grigor’yan and Jiaxin Hu: Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces, Inventiones Mathematicae 174 (2008), 81-126. A. Grigor’yan; 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. 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. A. Grigor’yan, 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. 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. A. Grigor’yan, 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. Kenneth J. Falconer and Jiaxin Hu: Nonlinear diffusion equations on unbounded fractal domains. J. Math. Anal. Appl. 256 (2001), 606–624. Jiaxin Hu and P.G. LeFloch: L1-continuous dependence property for systems of conservation laws, Arch. Rational Mech. Anal. 151 (2000), 45-93. Jiaxin Hu: The Riemann problem for pressureless ?uid dynamics with distribution solutions in Colombeau’s sense, Comm. Math. Phys, 194 (1998), 191-205. Book：《分形分析引论》，胡家信著，科学出版社，2013，230页。An introduction to fractal analysis (in Chinese, 230 pages), Science Press, 2013.