Mathematics is the language in which God has written the universe

Research Interests

• Mathematical Analysis

• Partial Differential Equations

• Mathematical Physics

Publications

*–Undergraduate Publication

• J. Flynn, N. Lam, G. Lu. L^p-Hardy identities and inequalities with respect to the distance and mean distance to the boundary. Calc. Var., 2024. 

• A.X. Do; N. Lam; G. Lu. A new approach to weighted Hardy-Rellich inequalities: improvements, symmetrization principle and symmetry breaking. J. Geom. Anal. 2024.

• C. Cazacu; D. Krejcirik; N. Lam; A. Laptev. Hardy inequalities for magnetic p-Laplacians. Nonlinearity 37 (2024), no. 3, 035004 (27 pp). 

• C. Cazacu; J. Flynn; N. Lam; G. Lu. Caffarelli-Kohn-Nirenberg identities, inequalities and their stabilities. J. Math. Pures Appl., 182 (2024) 253-284.

• * S. Kendell*; N. Lam; D. Smith*; A. White*; P. Wiseman*. A simple proof of the refined sharp weighted Caffarelli-Kohn-Nirenberg inequalities. AIMS Mathematics 2023, Volume 8, Issue 11: 27983-27988.

• N. Lam; G. Lu. Improved Lp-Hardy and Lp-Rellich inequalities with magnetic fields. Vietnam J. Math. (2023). https://doi.org/10.1007/s10013-023-00637-z.

• C. Cazacu; J. Flynn; N. Lam. Caffarelli-Kohn-Nirenberg inequalities for curl-free vector fields and second order derivatives. Calc. Var. 62 (2023), no. 4, 118

• N.A. Dao; N.T. Duy; N. Lam; N.V. Phong. Hardy-Sobolev Inequalities with Dunkl Weights. Acta Mathematica Vietnamica 48 (2023), no. 1, 133-149.

• J. Flynn; N. Lam; G. Lu; S. Mazumdar. Hardy’s identities and inequalities on CartanHadamard manifolds. J. Geom. Anal. 33 (2023), no. 1, Paper No. 27.

• * N.A. Dao; A. X. Do*; N.T. Duy; N. Lam. Hardy type identities on Rn-k × (R+)k via factorizations. Vietnam J. Math. 51 (2023), no. 2, 329–343.

• J. Flynn; N. Lam; G. Lu. Hardy-Poincare-Sobolev type inequalities on hyperbolic spaces and related Riemannian manifolds. J. Funct. Anal. 283 (2022), no. 12, Paper No. 109714, 37 pp.

• C. Cazacu; J. Flynn; N. Lam. Sharp second order uncertainty principles. J. Funct. Anal. 283 (2022), no. 10, Paper No. 109659.

• A.N. Dao; N. Lam; G. Lu. Gagliardo-Nirenberg type inequalities on Lorentz, Marcinkiewicz and weak-L∞ spaces. Proc. Amer. Math. Soc. 150 (2022), 2889-2900.

• N.T. Duy; N. Lam; G. Lu. p-Bessel pairs, Hardy’s identities and inequalities and HardySobolev inequalities with monomial weights. J. Geom. Anal. 32 (2022), no. 4, Paper No. 109, 36 pp.

• N.T. Duy; N. Lam; L.L. Phi. Improved Hardy inequalities and weighted Hardy type inequalities with spherical derivatives. Rev. Mat. Complut. 35 (2022), no. 1, 1–23.

• A.N. Dao; N. Lam; G. Lu. Gagliardo-Nirenberg and Sobolev interpolation inequalities on Besov spaces. Proc. Amer. Math. Soc. 150 (2022), no. 2, 605–616.

• N.T. Duy; N. Lam; L.L. Phi. Some Hardy identities on half-spaces. Math. Nachr. 294 (2021), no. 12, 2317–2328.

• C. Cazacu; J. Flynn; N. Lam. Short proofs of refined sharp Caffarelli-Kohn-Nirenberg inequalities. J. Differential Equations 302 (2021), 533–549.

• N.T. Duy; N. Lam; L.L. Phi. Sharp affine Trudinger-Moser inequalities: a new argument. Canad. Math. Bull. 64 (2021), no. 4, 765–778. 

• J. Flynn; N. Lam; G. Lu. Sharp Hardy Identities and Inequalities on Carnot Groups. Adv. Nonlinear Stud. 21 (2021), no. 2, 281–302

• A.N. Dao; S.G. Krantz; N. Lam. Cauchy integral commutators and Hardy factorization on Lorentz spaces. J. Math. Anal. Appl., 498 (2021), no. 1, 124926.

• N. Lam; P. Le. Quantum divergences with p-power means. Linear Algebra Appl., 609 (2021), 289–307

• N.T. Duy; N. Lam; L.L. Phi. A note on the second order geometric Rellich inequality on half-space. Monatsh. Math. 195 (2021), no. 2, 233–248

• N. Lam. Sharp weighted isoperimetric and Caffarelli-Kohn-Nirenberg inequalities. Adv. Calc. Var., 14 (2021), no. 2, 153–169

• N. Lam; R. Milley. Some notes on quantum Hellinger divergences with Heinz means. Electron. J. Linear Algebra, 36 (2020), 704-722

• N. Lam; G. Lu; L. Zhang. Geometric Hardy’s inequalities with general distance functions. J. Funct. Anal. 279 (2020), no. 8, 108673

• N.T. Duy; N. Lam; N.A. Triet. Improved Hardy and Hardy-Rellich type inequalities with Bessel pairs via factorizations. J. Spectr. Theory, 10 (2020), no. 4, 1277–1302

• * N.T. Duy; N. Lam; N.A. Triet; W. Yin*. Improved Hardy inequalities with exact remainder terms. Math. Inequal. Appl., 23 (2020), no. 4, 1205–1226

• N. Lam; G. Lu; L. Zhang. Factorizations and Hardy’s type identities and inequalities on upper half spaces. Calc. Var. Partial Differential Equations 58 (2019), no. 6, Art. 183, 31 pp

• N. Lam; G. Lu; L. Zhang. Existence and nonexistence of extremal functions for sharp Trudinger-Moser inequalities. Adv. Math. 352 (2019), 1253–1298

• N. Lam; G. Lu; L. Zhang. Sharp Singular Trudinger–Moser Inequalities Under Different Norms. Adv. Nonlinear Stud. 19 (2019), no. 2, 239–261

• N.T. Duy; N. Lam; N.A. Triet. Hardy-Rellich identities with Bessel pairs. Arch. Math. (Basel) 113 (2019), no. 1, 95–112

• N.T. Duy; N. Lam; N.A. Triet. Hardy and Rellich inequalities with exact missing terms on homogeneous groups. J. Math. Soc. Japan, Volume 71, Number 4 (2019), 1243-1256

• N. Lam; A. Maalaoui; A. Pinamonti. Characterizations of anisotropic high order Sobolev spaces. Asymptot. Anal. (2019) 113 (2019), no. 4, 239–260

• N. Lam. A note on Hardy inequalities on homogeneous groups. Potential Anal. 51 (2019), no. 3, 425–435

• N. Lam. General sharp weighted Caffarelli-Kohn-Nirenberg inequalities. Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), no. 3, 691–718

• M. Dong; N. Lam; G. Lu. Sharp weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg inequalities and their extremal functions. Nonlinear Anal. 173 (2018), 75–98

• N. Lam. Optimizers for the singular Trudinger-Moser inequalities in the critical case in R2. Math. Nachr. 291 (2018), no. 14–15, 2272–2287

• N. Lam; G. Lu. Weighted Moser-Onofri-Beckner and logarithmic Sobolev inequalities. J Geom Anal (2018) 28:1687–1715

• N. Lam. Hardy and Hardy-Rellich type inequalities with Bessel pairs. Ann. Acad. Sci. Fenn. Math. 43 (2018), 211–223

• N. Lam; G. Lu. Sharp constants and optimizers for a class of Caffarelli–Kohn–Nirenberg inequalities. Adv. Nonlinear Stud. 17 (2017), no. 3, 457–480

• N. Lam. Sharp Trudinger-Moser inequalities with monomial weights. NoDEA Nonlinear Differential Equations Appl. 24 (2017), no. 4, 24:39

• N. Lam. Equivalence of sharp Trudinger-Moser-Adams inequalities. Commun. Pure Appl. Anal. 16 (2017), no. 3, 973–997

• N. Lam. Maximizers for the singular Trudinger-Moser inequalities in the subcritical cases. Proc. Amer. Math. Soc. 145 (2017), no. 11, 4885–4892

• N. Lam; G. Lu; L. Zhang. Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities. Rev. Mat. Iberoam. 33 (2017), no. 4, 1219–1246

• N. Lam. Sharp subcritical and critical Trudinger-Moser inequalities on R2 and their extremal functions. Potential Anal. 46 (2017), no. 1, 75–103

• 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

• J. Bao; N. Lam; G. Lu. Polyharmonic equations with critical exponential growth in the whole space. Discrete Contin. Dyn. Syst. 36 (2016), no. 2, 577–600

• X. Cui; N. Lam; G. Lu. Characterizations of second order Sobolev spaces. Nonlinear Anal. 121 (2015), 241-261

• X. Cui; N. Lam; G. Lu. New characterizations of Sobolev spaces on the Heisenberg groups. J. Funct. Anal. 267 (2014), no. 8, 2962–2994

• 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

• N. Lam; G. Lu; H. Tang. Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs. Nonlinear Anal. 95 (2014) 77–92

• 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

• N. Lam; G. Lu. N–Laplacian equations in RN with subcritical and critical growth without the Ambrosetti-Rabinowitz condition. Adv. Nonlinear Stud. 13 (2013), no. 2, 289–308

• N. Lam; H. Tang. Sharp constants for weighted Moser-Trudinger inequalities on groups of Heisenberg type. Nonlinear Anal. 89 (2013) 95–109

• 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

• N. Lam; G. Lu. Sharp singular Adams inequalities in high order Sobolev spaces. Methods Appl. Anal. 19 (2012), no. 3, 243–266

• N. Lam; G. Lu. Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications. Adv. Math. 231 (2012) 3259–3287

• N. Lam; G. Lu; H. Tang. On nonuniformly subelliptic equations of Q–sub-Laplacian type with critical growth in the Heisenberg group. Adv. Nonlinear Stud. 12 (2012), 659–681

• 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

• N. Lam; G. Lu. Sharp Adams type inequalities in Sobolev spaces Wm,mn (Rn) for arbitrary integer m. J. Differential Equations 253 (2012), no. 4, 1143–1171.

• 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

• N. Lam; G. Lu. Existence and multiplicity of solutions to equations of N-Laplacian type with critical exponential growth in RN. J. Funct. Anal. 262 (2012) 1132–1165.

• * D.M. Duc; N.D. Hoang*; N. Lam*. Lagrange multipliers theorem and saddle point optimality criteria in mathematical programming. J. Math. Anal. Appl. 323 (2006), no. 1, 441–455.

Publications by Series

• N. Lam; G. Lu. Sharp singular Trudinger-Moser-Adams type inequalities with exact growth. Geometric methods in PDE’s, 43–80. Springer INdAM Ser., 13. Springer, Cham, 2015

• 1. N. Lam; G. Lu. The Moser-Trudinger and Adams Inequalities and Elliptic and Subelliptic Equations with Nonlinearity of Exponential Growth. Recent developments in geometry and analysis, 179–251. Adv. Lect. Math. (ALM), 23. International Press, Somerville, MA, 2012