# Qiang Xu

# Associate professor of Institute of Basic Mathematics.

# Email：xuq@lzu.edu.cn

# Ph.D.Lanzhou University, 2016, Mathematics

## Biography

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

## Publications

PUBLICATIONS 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. NEW FINISHED PAPERS 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.