1. 单变量复分析，拟共形映射，几何函数论及其在函数空间中的应用。

2. 椭圆偏微分方程，特别是跟变分问题相关。

3. 几何测度论，几何不等式的稳定性，自由边界问题。

招博士生（研究型），每年一至两个名额。

070101-基础数学

复分析，几何函数论
椭圆偏微分方程
变分问题

2014-08--2017-07   （芬兰）于韦斯屈莱大学   博士毕业
2013-08--2014-07   （芬兰）于韦斯屈莱大学   硕士毕业
2009-09--2013-06   北京航空航天大学   学士毕业

   

2019-08~2020-12,（瑞士）苏黎世联邦理工大学, 博士后
2017-08~2019-07,（德国）豪斯多夫数学研究中心, 博士后

单复变函数选讲

   

[1] Figalli, Alessio, Zhang, Yi RuYa. Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS[J]. 2024, 77(1): 3-36, http://dx.doi.org/10.1002/cpa.22132.
[2] Figalli, Alessio, Zhang Yi RuYa. Sharp gradient stability for the Sobolev inequality. DUKE MATHEMATICAL JOURNAL[J]. 2022, 171(12): 2407-2459, http://arxiv.org/abs/2003.04037.
[3] Yi RuYa Zhang. Duality of capacities and Sobolev extendability in the plane. COMPLEX ANALYSIS AND ITS SYNERGIES. 2021, 7(1): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7932497/.
[4] Zhang Yi. C1-Regularity of planar \infty-harmonic functions - revisited. Proc. Amer. Math. Soc.. 2020, 第 1 作者
[5] Figalli, Alessio, Zhang, Yi RuYa. Strong Stability for the Wulff Inequality with a Crystalline Norm. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS[J]. 2020, https://www.webofscience.com/wos/woscc/full-record/WOS:000546706300001.
[6] Zhang Yi. Second order regularity for equations involving p-Laplacian via a fundamental inequality. Adv. Math.. 2020, 第 1 作者
[7] Dong, Hongjie, Peng, Fa, Zhang, Yi RuYa, Zhou, Yuan. Hessian estimates for equations involving p-Laplacian via a fundamental inequality. ADVANCES IN MATHEMATICS[J]. 2020, 370: http://dx.doi.org/10.1016/j.aim.2020.107212.
[8] Zhang Yi. A variational characterization of the second eigenvalue of the p-Laplacian on quasi open sets. Proc. Lond. Math. Soc.. 2019, 第 1 作者
[9] Zhang Yi. Schoenfies solutions with conformal boundary values may fail to be Sobolev. Ann. Acad. Sci. Fenn. Math.. 2019, 第 1 作者  通讯作者  
[10] Zhang Yi. Some sharp Sobolev regularity for inhomogeneous \infty-Laplace equation in plane. J. Math. Pures Appl.. 2019, 第 1 作者
[11] Herbert Koch, Yi RuYa Zhang, Yuan Zhou. Some sharp Sobolev regularity for inhomogeneous infinity Laplace equation in plane. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. 2019, 132: 483-521, 
[12] Koskela Pekka, Rajala Tapio, Zhang Yi RuYa. A density problem for Sobolev spaces on Gromov hyperbolic domains. NONLINEAR ANALYSIS[J]. 2017, 154: 189-209, http://dx.doi.org/10.1016/j.na.2016.07.007.
[13] Koskela, Pekka, Zhang, Yi RuYa, Zhou, Yuan. Morrey-Sobolev Extension Domains. JOURNAL OF GEOMETRIC ANALYSIS[J]. 2017, 27(2): 1413-1434, http://dx.doi.org/10.1007/s12220-016-9724-9.
[14] Koskela, Pekka, Xiao, Jie, Zhang, Yi RuYa, Zhou, Yuan. A quasiconformal composition problem for the Q-spaces. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY[J]. 2017, 19(4): 1159-1187, http://dx.doi.org/10.4171/JEMS/690.
[15] Fusco, Nicola, Zhang, Yi RuYa. A quantitative form of Faber-Krahn inequality. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS[J]. 2017, 56(5): http://dx.doi.org/10.1007/s00526-017-1224-7.
[16] Koskela, Pekka, Zhang, Yi RuYa. A Density Problem for Sobolev Spaces on Planar Domains. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS[J]. 2016, 222(1): 1-14, http://dx.doi.org/10.1007/s00205-016-0994-y.
[17] Koch, Herbert, Zhang, Yi Ru-Ya, Zhou, Yuan. An asymtotic sharp Sobolev regularity for planar infinity harmonic functions. http://arxiv.org/abs/1806.01982.

   

（1）Stability of geometric inequalities in \mathbb R^n: Growth other than 2   2023-10-23
（2）Stability of geometric inequalities: Old and new   2023-05-29
（3） A generalization of quasiconformal reflections on the Riemann sphere   2019-11-24
（4）A fundamental inequality for the p-Laplacian and the infinity-Laplacian   2019-08-26
（5）Sobolev regularity of of infinity Laplace equations in the plane and its application   2019-06-24
（6） A geometric characterization for planar Sobolev extension domains   2016-05-29

现指导学生

苏伟聪  硕士研究生  070101-基础数学  

崔可泽  硕士研究生  070101-基础数学