Research

Publications
25. N. Lam General sharp weighted Caffarelli-Kohn-Nirenberg inequalities. Proc. Roy. Soc. Edinburgh Sect. A 2017.
24. N. Lam Equivalence of sharp Trudinger-Moser-Adams inequalities. Commun. Pure Appl. Anal. 2017. link
23. N. Lam Maximizers for the singular Trudinger-Moser inequalities in the subcritical cases. Proc. Amer. Math. Soc. 2017.  
22. N. Lam; G. Lu; L. Zhang Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities. Rev. Mat. Iberoam. 2017  
21. N. Lam Sharp subcritical and critical Trudinger-Moser inequalities on ℝ² and their extremal functions. Potential Analysis. 46 (2017), no. 1, 75–103. link
20. N. Lam; G. Lu; H. Tang Sharp affine and improved Moser-Trudinger-Adams type inequalities on unbounded domains in the spirit of Lions.  J. Geom. Anal. 27 (2017), no. 1, 300–334. link
19. J. Bao; N. Lam; G. Lu Polyharmonic equations with critical exponential growth in the whole spaceDiscrete Contin. Dyn. Syst.  36 (2016), no. 2, 577-600. link
18. X. Cui; N. Lam; G. Lu Characterizations of second order Sobolev spacesNonlinear Anal. 121 (2015), 241-261 link
17. X. Cui; N. Lam; G. Lu New characterizations of Sobolev spaces on the Heisenberg groups. J. Funct. Anal. 267 (2014), no. 8, 2962- 2994 link
16. N. Lam, G. Lu; H. Tang On sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs. Nonlinear Anal. 95 (2014) 77–92 link 
15. N. Lam; G. Lu Elliptic equations and systems with subcritical and critical exponential growth without the Ambrosetti-Rabinowitz condition. J. Geom. Anal. 24 (2014), no. 1, 118-143 link
14. N. Lam; G. Lu A new approach to sharp Moser-Trudinger and Adams type inequalities: a rearrangement-free argument. J. Differential Equations 255 (2013), no. 3, 298– 325 link
13. N. Lam; H. Tang Sharp constants for weighted Moser-Trudinger inequalities on groups of Heisenberg type. Nonlinear Anal.  89 (2013) 95–109 link
12. N. Lam; G. Lu N-Laplacian equations in with subcritical and critical growth without the Ambrosetti-Rabinowitz condition. Adv. Nonlinear Stud. 13 (2013), no. 2, 289–308 link
11. N. Lam; G. Lu Sharp singular Adams inequalities in high order Sobolev spaces. Methods Appl. Anal. 19 (2012), no. 3, 243-266 link
10. N. Lam; G. Lu Sharp Adams type inequalities in Sobolev spaces W^{m,n/m}(R^n) for arbitrary integer m. J. Differential Equations 253 (2012) 1143-1171 link
9. N. Lam; G. Lu Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications. Adv. Math.   231 (2012) 3259-3287 link
8. W. Cohn; N. Lam; G. Lu; Y. Yang The Trudinger-Moser inequality in unbounded domains of Heisenberg group and sub-elliptic equations.   Nonlinear Anal. 75 (2012), no. 12, 4483-4495 link
7. N. Lam, G. Lu; H. Tang On nonuniformly subelliptic equationsof Q-sub-Laplacian type with critical growth in the Heisenberg group.   Adv. Nonlinear Stud. 12 (2012), 659-681 link
6. N. Lam; G. Lu Existence of nontrivial solutions to Polyharmonic equations with subcritical and critical exponential growth.   Discrete Contin. Dyn. Syst. 32 (2012), no. 6, 2187–2205 link 
5. N. Lam; G. Lu Existence and multiplicity of solutions to equations of N-Laplacian type with critical exponential growth in R^N . J. Funct. Anal. 262 (2012) 1132- 1165 link 

Expository Papers
 4. N. Lam; G. Lu  Sharp Singular Moser-Trudinger-Adams Type Inequalities With Exact Growth. Springer INdAM SeriesA contribution to the special volume in honor of Ermanno Lanconelli. Geometric Methods in PDE’s, 43-80, 2015.  
 3. X. Cui; N. Lam; G. Lu  Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups. Appl. Math. J. Chinese Univ. Ser. B 28 (2013), no. 4, 531-547 link
 2. N. Lam; G. Lu  The Moser-Trudinger and Adams Inequalities and Elliptic and Subelliptic Equations with Nonlinearity of Exponential Growth. Recent Development in Geometry and Analysis, ALM 23, pp. 174–237, 2012.

Undergraduate Research
1. Duc, Duong M.; Hoang, Nguyen D.; Nguyen, Lam H. Lagrange multipliers theorem and saddle point optimality criteria in mathematical programming. J. Math. Anal. Appl. 323 (2006), no. 1, 441-455 link 

Thesis 

Collaborators
Grant
Reviewer for
AMS Mathematical Review
Memberships
+ AMS
+ SIAM
Elsewhere
+ My publications on Mathscinet.
+ Me on Research Gate.
+ Me on LinkedIn
+ Me on Academia

Research Interest
+ Calculus of Variations and PDEs
+ Geometric and Functional Inequalities
+ Sobolev spaces on Euclidean spaces, Heisenberg groups, metric spaces, etc
+ Optimal transport
Referee for the journals
+ Abstract and Applied Analysis + Acta Mathematica Sinica English Series + Advanced Nonlinear Studies
+ Boundary Value Problems + Calculus of Variations and PDEs Differential and Integral Equations
Journal of Function Spaces Journal of Inequalities and Applications + Mathematische Nachrichten 
+ Mathematical Problems in Engineering + Mathematica Scandinavica + Milan Journal of Mathematics 
+ Nonlinear Analysis TMA Proceedings of the London Mathematical Society
Research Awards
2014                Outstanding Achievement in Research, Wayne State University.
2012                Outstanding Graduate Research Award, Wayne State University.
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