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Qiang Xu

Associate professor of Institute of Basic Mathematics.


Ph.D.Lanzhou University, 2016, Mathematics


Birth: March 6, 1987 in Shaanxi Province, P.R. China.

• Lanzhou University, Lanzhou, Gansu, P.R. China. 
  Ph. D. in Fundamental Mathematics, July 2016
       •  Adviser: Zhongwei Shen & Peihao Zhao
       •  Dissertation: Regularity Estimates in Homogenization Theory of Elliptic Systems
M.S. in Fundamental Mathematics, July 2012
     •  Adviser: Peihao Zhao
B. S. in Information and Computational Mathematics, July 2009
• University of Kentucky, Lexington, KY, USA.
Joint Ph.D. Program in Mathematics, Aug. 2013- May 2015
     •  Adviser: Zhongwei Shen

Social experience

  • Teaching and guiding the situation of graduate students

  • Project results

  • Research interests

    Quantitative estimates in homogenization theory: 
    1.uniform regularity estimates; 
    2.convergence rates;
    3.homogenization of nonlinear elliptic operators, nonlocal operators; 
    4.boundary value problems on non-smooth domains.


    1. Q. Xu*, W. Zhao, S. Zhou, Commutator estimates for the Dirichlet-to-Neumann map of Stokes systems in Lipschitz domains, J. Math. Anal. Appl. 458 (2018), no.1, 219—241.
    2. S. Gu, Q. Xu*, Optimal boundary estimates for Stokes systems in homogenization theory, SIAM J. Math. Anal. 49 (2017), no.5, 3831—3853.
    3. Q. Xu, Convergence rates and  estimates in homogenization theory of Stokes systems in Lipschitz domains, J. Differential Equations 263 (2017), no.1, 398-450.
    4. Q. Xu, Convergence rates for general elliptic homogenization problems in Lipschitz domains. SIAM J. Math. Anal. 48 (2016), no.6, 3742—3788.
    5. Q. Xu, Uniform regularity estimates in homogenization theory of elliptic systems with lower order terms on the Neumann boundary problem, J. Differential Equations 261 (2016), no.8, 4368—4423.
    6. Q. Xu, Uniform regularity estimates in homogenization theory of elliptic system with lower order terms, J. Math. Anal. Appl. 438(2016), no.2, 1066—1107.
    7. Q. Xu*, S. Zhou, Lp Neumann problems in homogenization of general elliptic Systems, arXiv:1806.02632v1 (2018).
    8. Q. Xu*, P. Zhao, S. Zhou, The methods of layer potentials for general elliptic homogenization problems in Lipschitz domains, arXiv:1801.09220v1 (2018).
    9. Q. Xu*, S. Zhou, Quantitative estimates in homogenization of parabolic systems of elasticity in Lipschitz cylinders, arXiv:1705.01479v2 (2017).
    10. L. Wang, Q. Xu*, P. Zhao, Quantitative estimates on periodic homogenization of nonlinear elliptic operators. 
    *  Corresponding author
  • Honor and Award

  • 2017              Outstanding Doctoral Dissertations, Gansu Mathematical Society, P.R. China.
    2016              Boya Postdoctoral Fellowship, Peking University, P.R. China
    2009-2015    The First Prize Scholarship, Lanzhou University
    2008              National Scholarship, Ministry of Education of China.
    2007              The Second Prize in National Mathematical Modeling Contest, Ministry of Education of China.
  • Other information