ZHENG Shenzhou

Professional title:Professor

Office No.:+86-01051682054-118


  1.   June 1997, Ph. D., Institute of Mathematics, Fudan University, Shanghai, China
  2.   July 1994, M.S., Department of Mathematics, Beijing Normal University, Beijing, China
  3.   July 1986, B. S., Department of Mathematics, Taizhou College, Zhejiang, China

Professional Experience

ZHENG Shen Zhou is a professor and doctoral supervisor of Beijing Jiaotong University, with his research interests including the theory and applications of partial differential equations, uncertainty principle and special functions. He got Ph D from Fudan University in June 1997, from then on he  started his work period at School of Science of Beijing Jiaotong University. He ever visited University of Kentucky, University of Chicago, Purdue University, University of Texas in USA and Basque Center for Applied Mathematics in Spain,etc. Up yo now, he has published more than 130 papers including the well-known journals of Trans Amer Math Soc, J. Functional Anal, J. Differ Equ, Proc Amer Math Soc, etc. He has hosted 4 projects of the National Natural Science Foundation of China, and 1 project of CRRC "High-speed train Body Structure Dynamic model". He was awarded the title of Excellent Young Backbone Teacher of Beijing in 1998, the second prize of Excellent Young Paper of Beijing in 1999, the second prize of Science and Technology award of China Railway Society in 2014, and the Outstanding Paper Award of JMAA (Ames Award endorsed by American Mathematical Society) in 2020.  

Research Field

  1. Partial differential equations and their applications
  2. Uncertainty principle
  3. Special functions
  4. Geometric analysis


1. Jan.2021--Dec. 2024: Principal Investigator, "Regularity research for elliptic and parabolic equations with non-standard growths under assumptions of weak regular data" supported by the NSF of China (No. 12071021)

2. Sep.2016--Jan. 2018: Principal Investigator, "Harmonic analysis and Differential equations: New challenges" supported by the NSFC-ERC of China (No. 11611530539)

3. Jan.2014--Dec. 2017: Principal Investigator, "Some problems of parabolic and elliptic equations and systems" supported by the NSF of China (No. 11371050)

4. Jan.2011--Dec. 2013: Principal Investigator, "Regularity of nonlinear degenerate elliptic problems with discontinuous coefficients" supported by the NSF of China (No. 11071012)

5. Jan. 2007-Dec. 2009: Co-Investigator, "Nonlinear elliptic equations related to mean curvature" supported by the NSF of China (No. 10671022)


Teaching Courses

  • Undergraduate courses: Advanced Mathematics, Linear Algebra, Geometric Algebra, Spatial Analytic Geometry, Complex Functions and Integral Transformations, Mathematical and Physical Equations, Partial Differential Equations, Probability and Statistics, Computational Methods, Operations Research, etc.  
  • Postgraduate courses: Modern Theory of Partial Differential Equations, Sobolev Spaces, Functional Analysis, Elliptic Partial Differential Equations of Second Order, Partial Differential Equations of Parabolic Type, Numerical Analysis, Mathematical Statistics, Field theory, Special Functions, etc.  


Upto now, there are over 130 papers published in Trans. Amer. Math. Soc., Proc. Amer. Math. Soc., J. Func. Anal., J. Differ. Equ., Discrete Conti. Dyn. Syst., Nonlinear Anal., Dynamics Part. Diff. Equ., IMA J. Applied Math., Z. Angew. Math. Phys., J. Math. Anal. Appl., Electron. J. Differ. Equ., Diff. and Integral Equ., Comm. Pure Appl. Anal., ETC. Somce recent papers is selected as follows:

1. Liang S., Zheng S.Z., Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth. Adv. Nonlinear Anal. 10 (2021), no. 1, 172–193

2. Zhang X., Zheng S.Z., Besov regularity for the gradients of solutions to non-uniformly elliptic obstacle problems, J. Math. Anal. Appl. 504 (2021),123924

3. Liang S., Zheng S.Z., Lorentz estimates to nonlinear elliptic obstacle problems of p(x)-growth in Reifenberg domains, J. Math. Anal. Appl.501 (2021),125402

4. Hong T., Zheng S.Z., The W1,2(p,q)‑solvability for a class of fully nonlinear parabolic equations, J. Elliptic and Parabolic Equ. 7 (2021), no. 1, 25–45

5. Liang S., Zheng S.Z.,The Calderón–Zygmund estimates for a class of nonlinear elliptic equations with measure data. Math. Nachr. 294 (2021), no. 3, 603–615

6. Liang S., Zheng S.Z.,Calderón–Zygmund estimate for asymptotically regular elliptic equations with Lp(x)-logarithmic growth,Complex Var. and Elliptic Equ.,2021,

7. Zhu X., Zheng S.Z.,On uncertainty principle for the two-sided quaternion linear canonical transform, J. Pseudo-Differ. Oper. Appl. 12(1) (2021), Paper No. 3, 25 pp

8. Wang G., Zheng S.Z., Wang J., Nonlinear fluctuation behaviors of complex voter financial price dynamics on small-world network, Nonlinear Dyn. 103 (2021), 2525–2545

9. Zhu X., Zheng S.Z.,Uncertainty principles for the two-sided offset quaternion linear canonical transform, Math Meth Appl Sci. 2021;1–20; DOI: 10.1002/mma.7692

10. Zhang J., Zheng S.Z., Zuo C., W^{2,p}-regularity for asymptotically regular fully nonlinear elliptic and parabolic equations with oblique boundary values, Discrete Conti. Dyn. Syst. S. 14(9)(2021), 3305--3318

11. Zhang J., Zheng S.Z.,Yu, H., Lp(⋅)-regularity of Hessian for nondivergence parabolic and elliptic equations with measurable coefficients.Commun. Pure Appl. Anal. 19 (2020), no. 5, 2777–2796

12. Zhang J., Zheng S.Z., Feng Z., Weighted Lp(·)-regularity for fully nonlinear parabolic equations. Calc. Var. and PDE, (2020) 59:190

13. Zhang J., Zheng S.Z., Weighted gradient estimates for general nonlinear elliptic equations involving measure data, J. Math. Anal. Appl.488 (2020), no.1, 124048, 51pp

14. Liang S., Zheng S.Z., Variable Lorentz estimate for conormal derivative problems of stationary Stokes system with partially BMO coefficients, Nonlinear Anal. 194 (2020), 111355, 24 pp.

15. Tian H., Zheng S.Z., Orlicz estimates for general parabolic obstacle problems with p(t,x)-growth in Reifenberg domains, Electron. J. Differ. Equ. 2020, Paper No. 3, 25 pp.

16. Zhang J., Zheng S.Z., Sobolev regularity for quasilinear parabolic equations with asymptotically regular nonlinearity. Appl. Math. Lett. 103 (2020), 106211, 8 pp.

17. Zhang J., Zheng S.Z.,Hessian estimates for nondivergence parabolic and elliptic equations with partially BMO coefficients. Results Math. 75(1) (2020), Paper no. 21

18. Liang S., Zheng S.Z., Calderón-Zygmund estimate for asymptotically regular non-uniformly elliptic equations, J. Math. Anal. Appl. 484 (2020), no. 2,123749, 17pp.

19. Zhu X., Zheng S.Z., Uncertainty Principles for the Two-Sided Quaternion LinearCanonical Transform, Circuits, Systems, and Signal Processing (2020) 39:4436–4458.

20. S. Byun, S. Liang, Zheng S.Z., Nonlinear gradient estimates for double phase elliptic problems with irregular double obstacles, Proceedings of AMS,147(9), 2019

21. Liang S., Zheng S.Z.,On W1,γ(·)-regularity for nonlinear non-uniformly elliptic equations, manuscripta math. 159, (2019)

22. Liang S., Zheng S.Z.,Variable Lorentz estimate for conormal derivative problems of stationary Stokes system with partially BMO coefficients, Nonlinear Anal., 2019, 10.1016/

23. J. Zhang,M.Cai,Zheng S.Z., Weighted Lorentz estimate for asymptotically regular parabolic equations of p(x,t)-Laplacian type, Nonlinear Anal., 180 (2019), 225–235.

24. H. Tian, Zheng S.Z., Morrey regularity for nonlinear elliptic equations with partial BMO nonlinearities under controlled growth, Nonlinear Anal.,180 (2019)

25. H. Tian, Zheng S.Z.,Lorentz estimate with a variable power for parabolic obstacle problems with non-standard growths, J. Differ. Equ., 266(2019)

26. Liang S., Zheng S.Z.,Variable Lorentz estimate for stationary Stokes system with partially BMO coefficients, Commun. Pure Appl. Anal.18(6), 2019

27. Nonlinear Complexity and Chaotic Behaviors on Finite-Range Stochastic Epidemic Financial Dynamics, Intern. J. Bifu. Chaos, 29(6) (2019) (with G. Wang and J. Wang)

28. Lorentz estimates for asymptotically regular fully nonlinear parabolic equations, Math. Nachr., 291(2018) (with J. Zhang)

29. Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities, Nonlinear Anal., 172(2018) (with S. Liang)

30. Optimal Morrey estimate for parabolic equations in divergence form via Green's functions, Rocky Mountain J. Math., 48(6)(2018) (with J. Zhang)

31. Global regularity in Lorentz spaces for nonlinear elliptic equations with L^{p(\cdot)}\log L-growth, J. Math. Anal. Appl.,467(2018)(with S. Liang and M. Cai)

32. Weighted Lorentz and Lorentz–Morrey estimates to viscosity solutions of fully nonlinear elliptic equations, Complex Var. Elliptic Equ., 63(9),2018(with J. Zhang)

33. Orlicz estimates for nondivergence linear elliptic equations with partially BMO coefficients, Complex Var. Elliptic Equ., 63(6),2018 (with H. Li and J. Zhang)

34. Gradient estimate in Orlicz spaces for elliptic obstacle problems with partially BMO nonlinearities, Electron. J. Differ. Equ. Vol. 2018 (2018), No. 58(with S. Liang)

35. The monotonicity and convexity for the ratios of modified Bessel functions of the second kind and applications. Proceedings of AMS 145  (2017), no. 7(with Z. Yang)

36. Lorentz estimates for fully nonlinear parabolic and elliptic Equations. Nonlinear Anal. 148 (2017)(with J. Zhang)

37. Uniformly nondegenerate elliptic equations with partially BMO coefficients in nonsmooth domains.Nonlinear Anal.156 (2017)(with H.Tian)

38. Complex and Entropy of Fluctuations of Agent-Based Interacting Financial Dynamics with Random Jump. Entropy 2017, 19, 512 (With Y. Wang, W. Zhang and J. Wang)

39. Global weighted Lorentz estimates to nonlinear parabolic equations over nonsmooth domains, J. Math. Anal. Appl. 456 (2017)(H.Tian)

40. Sharp bounds for the ratio of modified Bessel functions, Mediterr. J. Math. (2017) 14:169 (with Z. Yang)

41. New sharp approximations involving incomplete gamma functions, Results Math.,72 ( 2017)(with T. Lou, H. Lv, Z.Yang)

42. Zheng S.Z., A compactness result for polyharmonic maps in the critical dimension. Czechoslovak Math. J. 66(141) (2016), no.1

43. Cheng C., Li W.,Wang Z.,Zheng S.Z. Traveling waves connecting equilibrium and periodic orbit for a delayed population model on a two-dimensional spatial lattice. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 26 (2016), no. 3, 1650049, 13 pp

44. Yu H., Zheng S.Z., Morrey estimates for subelliptic p-Laplace type systems with VMO coefficients in Carnot groups.Electron. J. Differ. Equ. 2016, Paper No. 33, 14 pp

45. Zhang J., Zheng S.Z., Lorentz estimate for nonlinear parabolic obstacle problems with asymptotically regular nonlinearities. Nonlinear Anal.134 (2016)

46. Zheng S.Z., Feng Z., Regularity of subelliptic p  -harmonic systems with subcritical growth in Carnot group. J. Diffe. Equ. 258 (2015), no. 7

47. Zheng S.Z., A strong convergence of the weak gradient to A-harmonic type operators with L1 data. J. Math. Anal. Appl. 430(2015), no.1

48. Yu H., Zheng S.Z., BMO estimate to A-harmonic systems with discontinuous coefficients. Nonlinear Anal. Real World Appl. 26 (2015)

49. Wang C., Zheng S.Z., Energy identity for a class of approximate biharmonic maps into sphere in dimension four. Discrete Contin. Dyn. Syst. 33 (2013), no. 2, 861–878

50. Feng Z., Tian J., Zheng S.Z., Lu H., Travelling wave solutions of the Burgers-Huxley equation. IMA J. Appl. Math. 77 (2012), no. 3, 316–325

51. Wang C., Zheng S.Z, Energy identity of approximate biharmonic maps to Riemannian manifolds and its application. J. Funct. Anal. 263 (2012), no. 4, 960–987

52. Zheng S.Z., Feng Z., Green functions for a class of nonlinear degenerate operators with X-ellipticity. Trans. Amer. Math. Soc. 364 (2012), no. 7, 3627–3655

53. Zheng S.Z., Zheng X., Feng Z., Optimal regularity for A -harmonic type equations under the natural growth. Discrete Contin. Dyn. Syst. B 16 (2011), no. 2, 669–685

54. Feng Z., Zheng, S. Z., Gao, David Y. Traveling wave solutions to a reaction-diffusion equation. Z. Angew. Math. Phys. 60 (2009), no. 4, 756–773

55. Feng Z., Zheng S.Z., Lu H., Green's function of non-linear degenerate elliptic operators and its application to regularity. Differ. Integral Equ. 21 (2008), no. 7-8, 717–741

56. Zheng S.Z., Zheng, X., Feng Z.,Regularity for a class of degenerate elliptic equations with discontinuous coefficients under natural growth. J. Math. Anal. Appl. 346(2) (2008), 359–373

57. Zheng S.Z., Feng Z. Regularity for quasi-linear elliptic systems with discontinuous coefficients. Dyn. Partial Differ. Equ. 5 (2008), no. 1, 87–99

58. Zheng S.Z., Zhang L.; Feng Z., Everywhere regularity for $p$ -harmonic type systems under the subcritical growth. Commun. Pure Appl. Anal. 7 (2008), no. 1, 107–117

Awards and honors

  • He was awarded the title of Excellent Young Backbone Teacher of Beijing in 1998 
  • The second prize of Excellent Young Paper of Beijing in 1999 
  • As a principal participant, he got the second prize of Science and Technology award of China Railway Society in 2014
  • He was awarded the Outstanding Paper of JMAA (Ames Award endorsed by American Mathematical Society) in 2020.