Truyen V. Nguyen

Associate Professor 
The University of Akron
Department of Mathematics
302 Buchtel Common
Akron, OH 44325-4002
Office: CAS 266
Phone: (330) 972-2569
Fax: (330) 374-8630
Email: tnguyen(at)uakron(dot)edu


Curriculum Vitae   Truyen Nguyen's CV


Research Interests

  • Partial Differential Equations, Calculus of Variations and Optimal Control
  • Monge-Kantorovich Mass Transportation, Fluid dynamics
  • Information theory

Publications

Book Chapters

  1. Interior Hölder Estimates for Second Derivatives (with C. Gutierrez and Q. Huang). This appears as Chapter 8 in the book
     "The Monge-Ampère Equation, Birkhäuser Verlag, 2016" by C. Gutierrez.

Preprints

  1. Stability estimates for SDEs and Fokker-Planck-Kolmogorov equations.
  2. Boundary regularity for quasilinear elliptic equations with general Dirichlet boundary data,  arXiv:1811.03947v1 

Published Articles

Papers on PDEs of elliptic and parabolic type:

  1. Regularity estimates in weighted Morrey spaces for quasilinear elliptic equations (with G. Di Fazio), To appear in  Revista  Matematica Iberoamericana,  arXiv:1810.12496v1
  2. Interior Calderón-Zygmund estimates for solutions to general parabolic equations of p-Laplacian type,  Calc. Var. Partial Differential Equations  56  (2017),  no. 6, Art. 173, 42 pp,  arXiv:1709.02847v1
  3. Global W^{1,p} estimates for solutions to the linearized Monge-Ampère equations (with N. Le), J. Geom. Anal.  27  (2017),  no. 3, 1751--1788, arXiv:1602.02194v1
  4. Interior gradient estimates for quasilinear elliptic equations (with T. Phan), Calc. Var. Partial Differential Equations  55  (2016),  no. 3, Art. 59, 33 pp.
  5. Local gradient estimates for degenerate elliptic equations (with L. Hoang and T. Phan), Adv. Nonlinear Stud.  16  (2016),  no. 3, 479--489, arXiv:1505.01122v1
  6. Interior second derivative estimates for solutions to the linearized Monge-Ampère equation (with C. Gutierrez), Trans. Amer. Math. Soc. 367 (2015), no. 7, 4537--4568,  arXiv:1208.5097v1
  7. Gradient estimates and global existence of smooth solutions to a cross-diffusion system (with L. Hoang and T. Phan), SIAM J. Math. Anal.  47  (2015),  no. 3, 2122--2177, arXiv:1311.6828v1
  8. A perturbation argument for a Monge-Ampère type equation arising in optimal transportations (with L. Caffarelli and M.d.M. González), Arch. Ration. Mech. Anal. 212 (2014), no. 2, 359--414.
  9. Global W^{2,p} estimates for solutions to the linearized Monge-Ampère equations (with N. Le),  Math. Ann.  358  (2014),  no. 3-4, 629--700, arXiv:1209.1998v2
  10. Geometric properties of boundary sections of solutions to the Monge-Ampère equation and applications (with N. Le),  J. Funct. Anal.  264  (2013),  no. 1, 337--361,  arXiv:1205.6882v1
  11. Interior gradient estimates for solutions to the linearized Monge-Ampère equation (with C. Gutierrez), Advances in Mathematics, vol. 228, 2034--2070, 2011.
  12. Weighted Sobolev's inequalities for bounded domains and singular elliptic equations (with D. M. Duc and N. C. Phuc) Indiana University Mathematics Journal, vol. 56, no. 2, 615--642, 2007.
  13. On Monge-Ampère type equations arising in optimal transportation problems (with C. E. Gutierrez) Calc. Var. Partial Differential Equations, vol. 28, no. 3, 275--316, 2007. 
  14. Homogenization and convergence of correctors in Carnot groups (with B. Franchi and C. E. Gutierrez) Comm. Partial Differential Equations, vol. 30, no. 10-12, 1817--1841, 2005.
 Papers on kinetic theory, conservation laws, and calculus of variations and HJEs in the Wasserstein space:
  1. One-dimensional pressureless gas systems with/without viscosity (with A. Tudorascu), Comm. Partial Differential Equations  40  (2015),  no. 9, 1619--1665.
  2. Erratum to: Global magnetic confinement for the 1.5D Vlasov-Maxwell system (with Toan Nguyen and W. Strauss), Kinet. Relat. Models  8  (2015),  no. 3, 615--616.
  3.  Global magnetic confinement for the 1.5D Vlasov-Maxwell system (with Toan Nguyen and W. Strauss), Kinet. Relat. Models  8  (2015), no. 1, 153--168, arXiv:1410.3003v1
  4. Non-existence and non-uniqueness for multidimensional sticky particle systems (with A. Bressan), Kinet. Relat. Models  7  (2014),  no. 2, 205--218,  arXiv:1312.1636v1
  5. Hamilton-Jacobi equations in space of measures associated with a system of conservation laws (with J. Feng), J. Math. Pures Appl. (9) 97 (2012), no. 4, 318--390.
  6. On the existence, uniqueness and stability of entropy solutions to scalar conservation laws (with D. Golovaty),  J. Differential Equations  253  (2012),  no. 5, 1341--1375.
  7. Hamilton-Jacobi equations in the Wasserstein space (with W. Gangbo and A. Tudorascu), Methods and Applications of Analysis, vol. 15, no. 2, 155--183, 2008.            
  8. Pressureless Euler/Euler-Poisson systems via adhesion dynamics and scalar conservation laws (with A. Tudorascu), SIAM J. Math. Analysis, vol. 40, no. 2, 754--775, 2008.
  9. Euler-Poisson systems as action-minimizing paths in the Wasserstein space (with W. Gangbo and A. Tudorascu), Arch. Rat. Mech. Analysis, vol. 192, no. 3, 419--452,
Papers on information theory:
  1. M. Vu, N. H. Tran, H. D. Tuan, T. V. Nguyen, and Duy H.N. Nguyena, "Optimal Signaling Schemes and Capacities of Non-Coherent Correlated MISO Channels under Per-Antenna Power Constraints", in IEEE Transactions on Communications PP(99):1-1 DOI:10.1109/tcomm.2018.2863391, August 2018.
  2. Ranjbar, N. H. Tran, T. V. Nguyen,  M. C. Gursoy, and H. Nguyen-Le, "Capacity-Achieving Signals for Point-to-Point and Multiple-Access Channels under Non-Gaussian Noise and Peak Power Constraint",  in IEEE Access PP(99):1-1 DOI:10.1109/ACCESS.2018.2837056,  May 2018.
  3. Ranjbar, N. H. Tran, T. V. Nguyen, and M. C. Gursoy, “Optimal Inputs of Single-User and Multi-User non-Gaussian Aggregate Interference Channels”, in Proc. IEEE Int. Conf. on Commun. (ICC) – Commun. Theory, Kansas, USA, May 2018, pp. 1-6.
  4. H. V. Vu, N. H. Tran, T. V. Nguyen, and S. I. Hariharan, “Estimating Shannon and Constrained Capacities of Bernoulli-Gaussian Impulsive Noise Channels in Rayleigh Fading”, IEEE Transactions on Communications, vol. 62 , pp. 1845-1856, June 2014.
  5. H. V. Vu, N. H. Tran, T. V. Nguyen, and S. I. Hariharan, “Estimating Information Rates of Bernoulli-Gaussian Impulsive Noise Channels in Rayleigh Fading”, in Proc. IEEE Int. Conf. on Commun. (ICC) – Wireless Commun., Sydney, Australia, Jun. 2014, pp. 5859-5864.
  6. H. V. Vu, N. H. Tran, T. V. Nguyen, and S. I. Hariharan, “On the Capacity of Bernouli-Gaussian Impulsive Noise Channels in Rayleigh Fading”, in Proc. IEEE Inter. Symp. on Personal, Indoor and Mobile Radio Commun. (PIMRC), London, UK, Sept. 2013, pp. 1281-1285.

Courses: Fall 2018

  • Math 3450:221 - Calculus I
  • Math 3450:625 - Real Analysis 

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