Works (54)

Updated: March 25th, 2025 16:42

2024 article

GENERIC PROPERTIES OF CONJUGATE POINTS IN OPTIMAL CONTROL PROBLEMS

Bressan, A., Mazzola, M., & Nguyen, K. t. (2024, September). MATHEMATICAL CONTROL AND RELATED FIELDS.

By: A. Bressan, M. Mazzola* & K. Nguyen n

author keywords: Optimal control problem; necessary optimality condition; conjugate point; generic property; Baire category
topics (OpenAlex): Aerospace Engineering and Control Systems; Optimization and Variational Analysis; Differential Equations and Boundary Problems
Sources: ORCID, Web Of Science
Added: September 23, 2024

2024 journal article

Piecewise regular solutions to scalar balance laws with singular nonlocal sources

Journal of Differential Equations.

author keywords: Piecewise smooth solutions; Scalar balance law; Singular kernels; Shock
topics (OpenAlex): Advanced Mathematical Physics Problems; Navier-Stokes equation solutions; Computational Fluid Dynamics and Aerodynamics
Sources: ORCID, Web Of Science, NC State University Libraries
Added: July 22, 2024

2023 review

A lower bound on the quantitative version of the transversality theorem

[Review of ]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 528(1).

author keywords: Transversality lemma; Quantitative estimates
topics (OpenAlex): Mathematical Dynamics and Fractals; Nonlinear Partial Differential Equations; Geometric Analysis and Curvature Flows
Sources: ORCID, Web Of Science
Added: August 14, 2023

2023 journal article

A quantitative version of the transversality theorem

Communications in Mathematical Sciences.

By: A. Murdza n & K. Nguyen n

topics (OpenAlex): Computability, Logic, AI Algorithms; semigroups and automata theory; Cellular Automata and Applications
Source: ORCID
Added: October 31, 2024

2023 article

Diffusion Approximations of Markovian Solutions to Discontinuous ODEs

Bressan, A., Mazzola, M., & Nguyen, K. T. (2023, March 5). JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS.

topics (OpenAlex): Stochastic processes and financial applications; Advanced Mathematical Modeling in Engineering; Nonlinear Partial Differential Equations
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
13. Climate Action (Web of Science)
Sources: ORCID, Web Of Science
Added: March 27, 2023

2023 article

EXAMPLES AND CONJECTURES ON THE REGULARITY OF SOLUTIONS TO BALANCE LAWS

Ancona, F., Bianchini, S., Bressan, A., Colombo, R. M., & Nguyen, K. T. (2023, February 8). QUARTERLY OF APPLIED MATHEMATICS.

topics (OpenAlex): Navier-Stokes equation solutions; Advanced Mathematical Physics Problems; Stability and Controllability of Differential Equations
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: ORCID, Web Of Science
Added: March 13, 2023

2023 article

Generic Properties of First-Order Mean Field Games

Bressan, A., & Nguyen, K. T. T. (2023, January 2). DYNAMIC GAMES AND APPLICATIONS, Vol. 1.

topics (OpenAlex): Stochastic processes and financial applications; Economic theories and models; Stochastic processes and statistical mechanics
Sources: Web Of Science, NC State University Libraries
Added: January 17, 2023

2023 article

STOCHASTIC EQUILIBRIUM SOLUTION FOR A DEBT MANAGEMENT PROBLEM WITH CURRENCY DEVALUATION

Marigonda, A., & Nguyen, K. T. (2023, May). MATHEMATICAL CONTROL AND RELATED FIELDS, Vol. 5.

author keywords: Stochastic model; infinite time horizon; optimal feedback solution; debt management; currency devaluation
topics (OpenAlex): Stochastic processes and financial applications; Differential Equations and Numerical Methods; Credit Risk and Financial Regulations
Sources: Web Of Science, NC State University Libraries
Added: June 19, 2023

2022 journal article

A system of first order Hamilton-Jacobi equations related to an optimal debt management problem

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 29(4).

author keywords: Hamilton-Jacobi equations; Viscosity solutions; Deterministic optimal debt management; Equilibrium solutions
topics (OpenAlex): Economic theories and models; Stochastic processes and financial applications; Monetary Policy and Economic Impact
Sources: ORCID, Web Of Science
Added: June 27, 2022

2022 article

Generalized Differential Games

Barron, E. N., & Nguyen, K. T. (2022, May 21). DYNAMIC GAMES AND APPLICATIONS.

By: E. Barron* & K. Nguyen n

author keywords: Differential games; Isaacs' equation; Generalized game; Hamilton-Jacobi; Viscosity solution; Control constraints
topics (OpenAlex): Economic theories and models; Optimization and Variational Analysis; Nonlinear Differential Equations Analysis
Sources: ORCID, Web Of Science
Added: May 31, 2022

2022 journal article

Metric Entropy for Hamilton--Jacobi Equations with Uniformly Directionally Convex Hamiltonian

SIAM Journal on Mathematical Analysis.

By: S. Bianchini, P. Dutta & K. Nguyen

topics (OpenAlex): Nonlinear Partial Differential Equations; Geometric Analysis and Curvature Flows; Navier-Stokes equation solutions
Source: ORCID
Added: August 15, 2024

2022 article

Shock interactions for the Burgers-Hilbert equation

Bressan, A., Galtung, S. T., Grunert, K., & Nguyen, K. T. (2022, June 24). COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, Vol. 6.

author keywords: Burgers-Hilbert equation; weak solution; piecewise regular solution; shock interaction
topics (OpenAlex): Gas Dynamics and Kinetic Theory; Navier-Stokes equation solutions; Computational Fluid Dynamics and Aerodynamics
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
13. Climate Action (Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: July 5, 2022

2021 journal article

METRIC ENTROPY FOR FUNCTIONS OF BOUNDED TOTAL GENERALIZED VARIATION

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 53(1), 1168–1190.

author keywords: metric entropy; doubling dimension; total generalized variation
topics (OpenAlex): Navier-Stokes equation solutions; Nonlinear Partial Differential Equations; Stability and Controllability of Differential Equations
TL;DR: A sharp estimate is established for a minimal number of binary digits needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space up to an accuracy of $\varepsilon>0$ with respect to the ${\bf L}^1$-distance. (via Semantic Scholar)
Sources: ORCID, Web Of Science
Added: March 29, 2021

2021 article

Markovian Solutions to Discontinuous ODEs

Bressan, A., Mazzola, M., & Nguyen, K. T. (2021, March 12). JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS.

topics (OpenAlex): Diffusion and Search Dynamics; Fluid Dynamics and Turbulent Flows; Stochastic processes and financial applications
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
13. Climate Action (Web of Science)
Sources: ORCID, Web Of Science
Added: April 5, 2021

2021 journal article

ON THE GLOBAL CONTROLLABILITY OF SCALAR CONSERVATION LAWS WITH BOUNDARY AND SOURCE CONTROLS

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 59(6), 4314–4338.

author keywords:   conservation laws; source control; global exact controllability; return method
topics (OpenAlex): Traffic control and management; Microbial metabolism and enzyme function; Navier-Stokes equation solutions
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: January 10, 2022

2021 journal article

SBV regularity for Burgers-Poisson equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 500(1).

author keywords: Burgers-Poisson equation; Entropy weak solution; SBV regularity
topics (OpenAlex): Nonlinear Waves and Solitons; Advanced Mathematical Physics Problems; Navier-Stokes equation solutions
Sources: Web Of Science, ORCID, NC State University Libraries
Added: April 19, 2021

2020 journal article

A model of debt with bankruptcy risk and currency devaluation

Minimax Theory and Its Applications. https://www.heldermann.de/MTA/MTA05/MTA052/mta05014.htm

Contributors: T. Nguyen

Source: ORCID
Added: October 31, 2024

2020 conference paper

Quantitative compactness estimate for scalar conservation laws with nonconvex fluxes

Hyperbolic problems: theory, numerics, applications, 248–255. AIMS Ser. Appl. Math., 10.

Contributors: T. Nguyen

Source: ORCID
Added: October 31, 2024

2019 journal article

APPROXIMATION OF SWEEPING PROCESSES AND CONTROLLABILITY FOR A SET-VALUED EVOLUTION

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 57(4), 2487–2514.

author keywords: sweeping processes; set-valued evolution; controllability
topics (OpenAlex): Optimization and Variational Analysis; Stability and Controllability of Differential Equations; Nonlinear Differential Equations Analysis
TL;DR: Under suitable assumptions, it is proved that there exists a control function such that the corresponding evolution of the set $\Omega(t)$ is arbitrarily close to the one determined by the sweeping process. (via Semantic Scholar)
Sources: ORCID, Web Of Science
Added: April 20, 2020

2019 book

Lyapunov’s Theorem via Baire Category

In Springer INdAM Series (Vol. 32, pp. 181–194).

Contributors: M. Mazzola* & K. Nguyen n

topics (OpenAlex): Optimization and Variational Analysis; Stability and Controllability of Differential Equations; Nonlinear Partial Differential Equations
Source: ORCID
Added: April 22, 2020

2019 journal article

ON KOLMOGOROV ENTROPY COMPACTNESS ESTIMATES FOR SCALAR CONSERVATION LAWS WITHOUT UNIFORM CONVEXITY

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 51(4), 3020–3051.

By: F. Ancona*, O. Glass* & K. Nguyen n

Contributors: F. Ancona*, O. Glass* & K. Nguyen n

author keywords: Kolmogorov entropy; scalar conservation laws; compactness estimates
topics (OpenAlex): Navier-Stokes equation solutions; Gas Dynamics and Kinetic Theory; Computational Fluid Dynamics and Aerodynamics
TL;DR: This paper provides an extension of quantitative compactness estimates to the case of scalar conservation laws with a smooth flux function that either is strictly (but not necessarily uniformly) convex or has a single inflection point with a polynomial degeneracy. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: ORCID, Web Of Science
Added: April 20, 2020

2018 journal article

Covering numbers for bounded variation functions

Journal of Mathematical Analysis and Applications, 468(2), 1131–1143.

Contributors: P. Dutta n & K. Nguyen n

author keywords: The epsilon-entropy; Bounded variation functions
topics (OpenAlex): Mathematical Approximation and Integration; Advanced Numerical Analysis Techniques; Machine Learning and Algorithms
TL;DR: Upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of epsilon with respect to ${\bf L}^1$-distance are provided. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries, Web Of Science
Added: October 16, 2018

2018 journal article

Stability of Feedback Solutions for Infinite Horizon Noncooperative Differential Games

DYNAMIC GAMES AND APPLICATIONS, 8(1), 42–78.

Contributors: A. Bressan* & K. Nguyen n

author keywords: Noncooperative differential games; Nash equilibrium; Infinite horizon
topics (OpenAlex): Economic theories and models; Mathematical Biology Tumor Growth; Optimization and Variational Analysis
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2017 journal article

A Stochastic Model of Optimal Debt Management and Bankruptcy

SIAM JOURNAL ON FINANCIAL MATHEMATICS, 8(1), 841–873.

Contributors: A. Bressan, A. Marigonda*, K. Nguyen n & M. Palladino*

author keywords: debt management and bankruptcy; infinite time horizon; optimal feedback solution
topics (OpenAlex): Economic theories and models; Stochastic processes and financial applications; Banking stability, regulation, efficiency
TL;DR: For a given bankruptcy threshold, existence and properties of optimal feedback strategies for the borrower are studied, in a stochastic framework as well as in a limit deterministic setting. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2017 journal article

Generalized Control Systems in the Space of Probability Measures

Set-Valued and Variational Analysis, 26(3), 663–691.

Contributors: G. Cavagnari*, A. Marigonda*, K. Nguyen n & F. Priuli*

author keywords: Optimal transport; Differential inclusions; Time-optimal control; Set-valued analysis
topics (OpenAlex): Stochastic processes and financial applications; Geometric Analysis and Curvature Flows; Markov Chains and Monte Carlo Methods
Sources: ORCID, Crossref, NC State University Libraries
Added: June 30, 2019

2016 journal article

An equilibrium model of debt and bankruptcy

ESAIM: Control, Optimisation and Calculus of Variations, 22(4), 953–982.

Contributors: A. Bressan* & K. Nguyen*

author keywords: Optimal control; differential game; optimal debt management; bankruptcy risk
topics (OpenAlex): Stochastic processes and financial applications; Economic theories and models; Banking stability, regulation, efficiency
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2016 journal article

COMPACTNESS ESTIMATES FOR HAMILTON-JACOBI EQUATIONS DEPENDING ON SPACE

Bulletin of the Institute of Mathematics Academia Sinica. https://www.math.sinica.edu.tw/bulletins/20161/2016104.pdf

Contributors: T. Nguyen

Source: ORCID
Added: October 31, 2024

2016 journal article

Global existence of weak solutions for Burgers-Poisson equation

Journal of Differential Equations, 23(4), 23–46.

By: T. Nguyen & K. Grunert

Source: NC State University Libraries
Added: June 30, 2019

2016 journal article

On the Burgers–Poisson equation

Journal of Differential Equations, 261(6), 3220–3246.

Contributors: K. Grunert* & K. Nguyen*

author keywords: Burgers-Poisson equation; Existence; Uniqueness; Blow-up
topics (OpenAlex): Nonlinear Waves and Solitons; Advanced Mathematical Physics Problems; Navier-Stokes equation solutions
Sources: ORCID, Crossref, NC State University Libraries
Added: April 22, 2020

2016 journal article

The bang–bang theorem via Baire category: a dual approach

Nonlinear Differential Equations and Applications NoDEA, 23(4).

topics (OpenAlex): Optimization and Variational Analysis; Advanced Optimization Algorithms Research; Stability and Controllability of Differential Equations
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2016 journal article

The compactness estimates for Hamilton Jacobi Equations depending on space

Bulletin of the Institute of Mathematics, Academia Sinica, 11, 63–113.

By: T. Nguyen, F. Ancona & P. Cannarsa

Source: NC State University Libraries
Added: June 30, 2019

2015 journal article

Conservation law models for traffic flow on a network of roads

Networks and Heterogeneous Media, 10(2), 255–293.

By: A. Bressan & K. Nguyen*

Contributors: A. Bressan & K. Nguyen*

author keywords: Traffic flows; network of roads; scalar conservation laws; Hamilton Jacobi equations; Lax type formula
topics (OpenAlex): Traffic control and management; Transportation Planning and Optimization; Evacuation and Crowd Dynamics
TL;DR: A model of traffic flow near an intersection, where drivers seeking to enter a congested road wait in a buffer of limited capacity, achieves well-posedness for general $L^\infty $ data, and continuity w.r.t. weak convergence of the initial densities. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2015 journal article

On compactness estimates for general nonlinear system hyperbolic systems

Annales De l'Institut Henri Poincaré, Analyse Non Linéaire, 32(6), 1229–1257.

By: T. Nguyen, F. Ancona & O. Glass

Source: NC State University Libraries
Added: July 28, 2019

2015 journal article

On compactness estimates for hyperbolic systems of conservation laws

Annales De l'Institut Henri Poincare (C) Non Linear Analysis, 32(6), 1229–1257.

By: F. Ancona*, O. Glass* & K. Nguyen*

Contributors: F. Ancona*, O. Glass* & K. Nguyen*

author keywords: Hyperbolic systems of conservation laws; Temple systems; Compactness estimates; Kolmogorov entropy
topics (OpenAlex): Navier-Stokes equation solutions; Advanced Mathematical Physics Problems; Geometric Analysis and Curvature Flows
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: ORCID, Crossref, NC State University Libraries
Added: April 22, 2020

2015 journal article

Optima and equilibria for traffic flow on networks with backward propagating queues

Networks and Heterogeneous Media, 10(4), 717–748.

Contributors: A. Bressan* & K. Nguyen*

author keywords: Traffic flows; network of roads; scalar conservation laws; global optima; Nash equilibria
topics (OpenAlex): Traffic control and management; Transportation Planning and Optimization; Evacuation and Crowd Dynamics
TL;DR: Two main results are proved: the existence of a globally optimal solution, minimizing the sum of the costs to all drivers, and the existenceof a Nash equilibrium solution, where no driver can lower his own cost by changing his departure time or the route taken to reach destination. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2015 journal article

Optimality conditions and regularity results for time optimal control problems with differential inclusions

Journal of Mathematical Analysis and Applications, 427(1), 202–228.

author keywords: Proximal normal vectors; Differential inclusions; Time optimal control; Semiconcave functions
topics (OpenAlex): Optimization and Variational Analysis; Nonlinear Partial Differential Equations; Contact Mechanics and Variational Inequalities
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2015 journal article

Quantitative Compactness Estimates for Hamilton–Jacobi Equations

Archive for Rational Mechanics and Analysis, 219(2), 793–828.

topics (OpenAlex): Navier-Stokes equation solutions; Mathematical Biology Tumor Growth; Stochastic processes and financial applications
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: ORCID, Crossref, NC State University Libraries
Added: June 30, 2019

2014 chapter

BV Regularity and Differentiability Properties of a Class of Upper Semicontinuous Functions

In I. Lirkov, S. Margenov, & J. Waśniewski (Eds.), Large-Scale Scientific Computing: Vol. 8353 LNCS (pp. 116–124).

Ed(s): I. Lirkov, S. Margenov & J. Waśniewski

topics (OpenAlex): Optimization and Variational Analysis; Advanced Mathematical Modeling in Engineering; Nonlinear Partial Differential Equations
TL;DR: A class of upper semicontinuous functions whose hypograph satisfies a geometric regularity property, namely: there exist \(\theta \in ]0,1] such that for each \(P\) on the boundary of \(\mathrm {hypo}\,f\) there exists a unitary Frechet (outer) normal. (via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: April 22, 2020

2014 journal article

Global Existence of Weak Solutions for the Burgers--Hilbert Equation

SIAM Journal on Mathematical Analysis, 46(4), 2884–2904.

By: A. Bressan & K. Nguyen*

Contributors: A. Bressan & K. Nguyen*

author keywords: Burgers-Hilbert equations; weak entropy solutions; global existence
topics (OpenAlex): Advanced Mathematical Physics Problems; Navier-Stokes equation solutions; Stability and Controllability of Differential Equations
TL;DR: This paper establishes the global existence of weak solutions to the Burgers--Hilbert equation, for general initial data in L for positive times, and a partial uniqueness result is proved for spatially periodic solutions. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2014 conference paper

On quantitative compactness estimates for hyperbolic conservation laws

Hyperbolic problems: theory, numerics, applications, 249–257, AIMS Ser. Appl. Math., 8, Am. Inst. Math. Sci. (AIMS), Springfield, MO,

Tien Khai Nguyen

Source: ORCID
Added: April 22, 2020

2013 journal article

Non-Lipschitz points and the SBV regularity of the minimum time function

Calculus of Variations and Partial Differential Equations, 51(1-2), 439–463.

topics (OpenAlex): Advanced Differential Equations and Dynamical Systems; Mathematical Dynamics and Fractals; Control and Stability of Dynamical Systems
Sources: ORCID, Crossref, NC State University Libraries
Added: July 9, 2019

2013 journal article

On the minimum time function around the origin

Mathematical Control and Related Fields, 3(1), 51–82.

Contributors: G. Colombo* & K. Nguyen*

author keywords: Reachable sets; exterior sphere condition; maximum principle
topics (OpenAlex): Advanced Differential Equations and Dynamical Systems; Control and Stability of Dynamical Systems; Advanced Differential Geometry Research
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2013 journal article

Some regularity results for a class of upper semicontinuous functions

Indiana University Mathematics Journal, 62(1), 45–89.

author keywords: exterior sphere condition; sets with positive reach; reduced boundary
topics (OpenAlex): Optimization and Variational Analysis; Point processes and geometric inequalities; Stability and Controllability of Differential Equations
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2012 journal article

Lower compactness estimates for scalar balance laws

Communications on Pure and Applied Mathematics, 65(9), 1303–1329.

By: F. Ancona*, O. Glass* & K. Nguyen*

Contributors: F. Ancona*, O. Glass* & K. Nguyen*

topics (OpenAlex): Navier-Stokes equation solutions; Stability and Controllability of Differential Equations; Advanced Mathematical Physics Problems
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2012 journal article

Rectifiability of special singularities of non-lipschitz functions

Journal of Convex Analysis, 19(1), 159–170. http://www.scopus.com/inward/record.url?eid=2-s2.0-84856829336&partnerID=MN8TOARS

By: T. Nguyen & D. Vittone

Contributors: K. Nguyen & D. Vittone

Sources: NC State University Libraries, ORCID
Added: July 28, 2019

2012 journal article

Singular gradient flow of the distance function and homotopy equivalence

Mathematische Annalen, 356(1), 23–43.

topics (OpenAlex): Geometric Analysis and Curvature Flows; Topological and Geometric Data Analysis; Homotopy and Cohomology in Algebraic Topology
Sources: ORCID, Crossref, NC State University Libraries
Added: June 30, 2019

2011 journal article

Exterior Sphere Condition and Time Optimal Control for Differential Inclusions

SIAM Journal on Control and Optimization, 49(6), 2558–2576.

By: P. Cannarsa* & K. Nguyen

Contributors: P. Cannarsa* & K. Nguyen

author keywords: proximal normal vectors; exterior sphere condition; differential inclusions; time optimal control; semiconcave functions
topics (OpenAlex): Stability and Controllability of Differential Equations; Optimization and Variational Analysis; Control and Dynamics of Mobile Robots
TL;DR: It is proved that the hypograph of $T(\cdot)$ satisfies, locally, an exterior sphere condition, which ensures most of the regularity results that hold for semiconcave functions, without assuming $T \cdot$ to be Lipschitz. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2010 journal article

Hypographs satisfying an external sphere condition and the regularity of the minimum time function

Journal of Mathematical Analysis and Applications, 372(2), 611–628.

Contributors: K. Nguyen*

author keywords: Normal vectors; phi-convex (prox-regular, positive reach) sets; Internal/external sphere condition
topics (OpenAlex): Optimization and Variational Analysis; Mathematical Dynamics and Fractals; Nonlinear Partial Differential Equations
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2010 journal article

On the Structure of the Minimum Time Function

SIAM Journal on Control and Optimization, 48(7), 4776–4814.

Contributors: G. Colombo* & K. Nguyen*

author keywords: normal vectors; phi-convex (prox-regular, positive reach) sets; internal sphere condition; small time controllability; adjoint flow
topics (OpenAlex): Optimization and Variational Analysis; Geometric Analysis and Curvature Flows; Numerical methods in inverse problems
TL;DR: It is shown thathypo(T) is $\varphi-convex$- Convex, i.e., satisfies a strong external sphere condition, and is a.e. twice differentiable and satisfies some further regularity properties. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2009 journal article

Quantitative isoperimetric inequalities for a class of nonconvex sets

Calculus of Variations and Partial Differential Equations, 37(1-2), 141–166.

Contributors: G. Colombo* & K. Nguyen*

author keywords: Sets with positive reach; External sphere condition; Internal cone condition; Isoperimetric deficiency; Spherical deviation; Fraenkel asymmetry
topics (OpenAlex): Point processes and geometric inequalities; Optimization and Variational Analysis; Advanced Optimization Algorithms Research
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019

2007 journal article

CRITICAL POINTS OF NON-C2 FUNCTIONALS

Topological Methods in Nonlinear Analysis.

Tien Khai Nguyen

Source: ORCID
Added: April 22, 2020

2007 journal article

Critical points of non-C2 functional

Topological Methods of Nonlinear Analysis, 29(1), 35–68.

By: T. Nguyen, D. Duong & H. Tran

Source: NC State University Libraries
Added: July 9, 2019

2007 journal article

Morse-Palais Lemma for nonsmooth functionals on normed spaces

Proceedings of the American Mathematical Society, 135(3), 921–927.

By: T. Nguyen, D. Duong & H. Tran

Source: NC State University Libraries
Added: July 28, 2019

2007 journal article

Morse-palais lemma for nonsmooth functionals on normed spaces

Proceedings of the American Mathematical Society, 135(3), 921–927.

By: D. Duc*, T. Hung* & N. Khai*

Contributors: D. Duc*, T. Hung* & N. Khai*

author keywords: Morse-Palais lemma; normed spaces; directional differentiability
topics (OpenAlex): Advanced Mathematical Modeling in Engineering; Nonlinear Partial Differential Equations; Advanced Numerical Methods in Computational Mathematics
Source: ORCID
Added: April 22, 2020

Employment

Updated: September 8th, 2019 18:32

North Carolina State Univeristy Raleigh, US
Department of Mathematics

Funding History

Funding history based on the linked ORCID record. Updated: October 31st, 2024 11:05

grant September 1, 2022 - August 1, 2025
Generic Singularities and Fine Regularity Structure for Nonlinear Partial Differential Equations
NSF
grant August 1, 2022 - July 1, 2023
40th Southeastern-Atlantic Regional Conference on Differential Equations
NSF
grant September 1, 2017 - August 1, 2022
Nonlinear PDEs, Differential Games and Applications
Simons Foundation

Citation Index includes data from a number of different sources. If you have questions about the sources of data in the Citation Index or need a set of data which is free to re-distribute, please contact us.

Certain data included herein are derived from the Web of Science© and InCites© (2025) of Clarivate Analytics. All rights reserved. You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.