Personal Information

Name:  Lu Chen (陈露)

Born:  February 14, 1992, Huainan, China

Email:  luchen@sns.it  chenlu5818804@163.com

Institute:  School of Mathematics and Statistics, BIT, 102400, China

Address: No.5 Zhongguancun South Street, Haidian District, Beijing, China

Educational Background

► 09/2013--06/2018, PhD in Pure Mathematics, School of Mathematics, Beijing Normal University. Major: Harmonic analysis and applications.

► 09/2009--08/2013, Bachelor in Mathematics, Anhui Normal University, China. 

Working Experience

► 09/2018--Present, Assistant Professor, School of Mathematics and Statistics, Beijing Institute of Technology.

Teachings

► 09/2016--2017.08, Teaching Advanced Mathematics in China University of Geosciences.

► 09/2018--2019.01, Assistant Professor, Teaching Advanced Mathematics for overseas students in Beijing Institute of Technology.

Publications

[1] L. Chen, G. Lu and M. Zhu: Existence and nonexistence of extremals for critical Adams inequalities in R4 and Trudinger-Moser inequalities in R2. Adv. Math. 368 (2020), 107143, 61 pp.

[2] L. Chen, Z. Liu , G. Lu and C. Tao: Stein-Weiss inequalities with the fractional Poisson kernel, Rev. Mat. Iberoam (2020), doi: 10.4171/RMI/1167.

[3] L. Chen, G. Lu and C. Zhang: Maximizers for fractional Caffarelli-Kohn-Nirenberg and Trudinger-Moser inequalities on the fractional Sobolev spaces, J. Geom. Anal, (2020), doi:10.1007/s12220-020-00406-1.

[4] X. Wang, L.Chen: Sharp weighted Trudinger-Moser inequalities with the L^n norm in the entire space and existence of their extremals, Potential analysis, (2020), doi:10.1007/s11118-019-09821-8.

[5] C. Zhang, J. Li and L. Chen: Ground state solutions of polyharmonic equations with potentials of positive low bound. Pacific J. Math. 305 (2020), no. 1, 353–384. 

[6] L. Chen and Z. Liu: Classification of solutions for an integral system with negative exponents on half space, Applicable Analysis, (2020), doi:10.1080/00036811.2020.1770735.

[7] L. Chen, G. Lu and C. Zhang: Sharp weighted Trudinger-Moser-Adams inequalities on the whole space and the existence of their extremals. Calc. Var. Partial Differential Equations 58 (2019), no. 4.

[8] L. Chen, G. Lu and C. Tao: Existence of extremal functions for the Stein-Weiss inequalities on the Heisenberg group. J. Funct. Anal. 277 (2019), no. 4, 1112–1138.

[9] L. Chen, G. Lu and C. Tao: Reverse Stein-Weiss inequalities on the upper half space and the existence of their extremals. Adv. Nonlinear Stud. 19 (2019), no. 3, 475–494.

[10] L. Chen, G. Lu and C. Tao: Hardy-Littlewood-Sobolev inequalities with the fractional Poisson kernel and their applications in PDEs. Acta Math. Sin. (Engl. Ser.) 35 (2019), no. 6, 853–875. 

[11] L. Chen, G. Lu and C. Tao: Reverse Stein-Weiss inequalities and existence of their extremal functions. Trans. Amer. Math. Soc. 370 (2018), no. 12, 8429–8450.

Visiting Positions

► 09/2019--Present, Visiting Scholar, Mathematics and information Science, Scuola Normale Superiore, Co-mentor: Prof. Andrea Malchiodi.

Awards, Honors and Recognitions

►  Outstanding PhD graduate of Beijing Normal University in 2018.

►  Excellent doctorial dissertation of Beijing Normal Univerisity in 2019.

Conference Talks and Invited Presentations

► Jul. 2–7, 2018: Existence of extremals for Caffarelli-Kohn-Nirenberg and Moser-Trudinger inequalities in the fractional Sobolev-Slobodeckij spaces, International Workshop on Singular Integral Operators in Tianjin, Nankai University, Tianjin, China.

►Nov. 10–13, 2016: Stein-Weiss inequalities with the fractional Poisson kernel, Conference on Harmonic Analysis and Its Applications in Beijing, Beijing Normal University, Beijing, China.

►May. 22–25,2015:The boundedness of multi-parameter pseudo-differential operators on multiparameter Sobolev spaces, Conference on Harmonic Analysis and Its Applications in Wuhan, Central China Normal University, Wuhan, China.

Fundings

► 01/2018--12/2020,National Natural Science Foundation of China (NSFC) (Grant No.：11701032), Principal Investigator.

► 01/2018--12/2020,National Natural Science Foundation of China (NSFC) (Grant No.：11701030), Principal Investigator.

Research Interests:

► Harmonic Analysis and its applications in PDEs.

► Sharp constants of geometrical inequalities (including HLS inequality, Caffarelli-Kohn-Nirenberg inequalities, Trudinger-Moser inequality) and existence/ non-existence of their extremals.

► Existence, Uniquenss, Concentrating behaviors and quantitative properties for the least energy solutions of Schordinger equation with the exponential non-linearity.

► Fractional Laplacian and the Methods of moving-plane.

► Conformal geometry and Variational PDEs.