## Bardi, Martino

Compute Distance To:
 Author ID: bardi.martino Published as: Bardi, Martino; Bardi, M.
 Documents Indexed: 82 Publications since 1981, including 3 Books 3 Contributions as Editor Co-Authors: 37 Co-Authors with 68 Joint Publications 1,132 Co-Co-Authors
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### Co-Authors

 12 single-authored 10 Cesaroni, Annalisa 9 Soravia, Pierpaolo 6 Alvarez, Olivier 5 Capuzzo Dolcetta, Italo 5 Da Lio, Francesca 4 Mannucci, Paola 3 Dragoni, Federica 3 Falcone, Maurizio 3 Sartori, Caterina 2 Badiale, Marino 2 Bagagiolo, Fabio 2 Bottacin, Sandra 2 Caines, Peter Edwin 2 Cirant, Marco 2 Feleqi, Ermal 2 Goatin, Paola 2 Goffi, Alessandro 2 Marchi, Claudio 2 Perthame, Benoît 1 Achdou, Yves 1 Cardaliaguet, Pierre 1 Evans, Lawrence Craig 1 Faggian, Silvia 1 Ghilli, Daria 1 Giga, Yoshikazu 1 Ishii, Hitoshi 1 Koike, Shigeaki 1 Maldonado López, Juan Pablo 1 Manca, Luigi 1 Osher, Stanley Joel 1 Parthasarathy, Thiruvenkatachari 1 Priuli, Fabio Simone 1 Raghavan, Tirukkannamangai E. S. 1 Rossi, Luca 1 Scotti, Andrea 1 Staicu, Vasile 1 Terrone, Gabriele 1 Topp, Erwin
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### Serials

 6 SIAM Journal on Control and Optimization 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Journal of Differential Equations 3 Communications on Pure and Applied Analysis 3 Dynamic Games and Applications 2 Journal of Mathematical Biology 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 SIAM Journal on Mathematical Analysis 2 Calculus of Variations and Partial Differential Equations 2 NoDEA. Nonlinear Differential Equations and Applications 2 Discrete and Continuous Dynamical Systems 2 Nonlinear Analysis. Theory, Methods & Applications 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 Funkcialaj Ekvacioj. Serio Internacia 1 Indiana University Mathematics Journal 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 Rendiconti del Seminario Matematico 1 Acta Applicandae Mathematicae 1 Asymptotic Analysis 1 Forum Mathematicum 1 Differential and Integral Equations 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Communications in Partial Differential Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Advances in Mathematical Sciences and Applications 1 Set-Valued Analysis 1 Journal of Convex Analysis 1 European Journal of Control 1 Annals of the International Society of Dynamic Games 1 Systems & Control: Foundations & Applications 1 Networks and Heterogeneous Media 1 Bollettino dell’Unione Matematica Italiana. Series IX 1 SIAM Journal on Financial Mathematics 1 Set-Valued and Variational Analysis 1 Modern Birkhäuser Classics
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### Fields

 57 Calculus of variations and optimal control; optimization (49-XX) 52 Partial differential equations (35-XX) 32 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 22 Systems theory; control (93-XX) 7 Ordinary differential equations (34-XX) 6 Probability theory and stochastic processes (60-XX) 4 Biology and other natural sciences (92-XX) 3 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 2 Integral equations (45-XX) 2 Mechanics of particles and systems (70-XX) 2 Operations research, mathematical programming (90-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) 1 Fluid mechanics (76-XX)

### Citations contained in zbMATH Open

77 Publications have been cited 1,645 times in 1,244 Documents Cited by Year
Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Zbl 0890.49011
Bardi, Martino; Capuzzo-Dolcetta, Italo
1997
Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Reprint of the 1997 original. Zbl 1134.49022
Bardi, Martino; Capuzzo-Dolcetta, Italo
2008
On Hopf’s formulas for solutions of Hamilton-Jacobi equations. Zbl 0569.35011
Bardi, M.; Evans, L. C.
1984
On the strong maximum principle for fully nonlinear degenerate elliptic equations. Zbl 0939.35038
Bardi, Martino; Da Lio, Francesca
1999
Explicit solutions of some linear-quadratic mean field games. Zbl 1268.91017
Bardi, Martino
2012
Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations. Zbl 1209.35001
Alvarez, Olivier; Bardi, Martino
2010
An approximation scheme for the minimum time function. Zbl 0723.49024
Bardi, M; Falcone, M.
1990
Singular perturbations of nonlinear degenerate parabolic pDEs: A general convergence result. Zbl 1032.35103
Alvarez, Olivier; Bardi, Martino
2003
Linear-quadratic $$N$$-person and mean-field games with ergodic cost. Zbl 1308.91008
Bardi, Martino; Priuli, Fabio S.
2014
Viscosity solutions methods for singular perturbations in deterministic and stochastic control. Zbl 1017.49028
Alvarez, Olivier; Bardi, Martino
2001
A boundary value problem for the minimum-time function. Zbl 0682.49034
Bardi, Martino
1989
Mean field games models of segregation. Zbl 1355.91003
Achdou, Yves; Bardi, Martino; Cirant, Marco
2017
Predator-prey models in periodically fluctuating environments. Zbl 0466.92019
Bardi, Martino
1981
The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations. Zbl 0733.35073
Bardi, Martino; Osher, Stanley
1991
Numerical methods for pursuit-evasion games via viscosity solutions. Zbl 1018.49027
Bardi, Martino; Falcone, Maurizio; Soravia, Pierpaolo
1999
Hamilton-Jacobi equations with singular boundary conditions on a free boundary and applications to differential games. Zbl 0732.35013
Bardi, Martino; Soravia, Pierpaolo
1991
On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations. Zbl 1142.35041
Bardi, Martino; Mannucci, Paola
2006
On the Bellman equation for some unbounded control problems. Zbl 0894.49017
Bardi, Martino; Da Lio, Francesca
1997
Nonlinear elliptic systems and mean-field games. Zbl 1358.35198
Bardi, Martino; Feleqi, Ermal
2016
Multiscale problems and homogenization for second-order Hamilton-Jacobi equations. Zbl 1133.35005
Alvarez, Olivier; Bardi, Martino; Marchi, Claudio
2007
Invariant sets for controlled degenerate diffusions: A viscosity solutions approach. Zbl 0928.93067
Bardi, Martino; Goatin, Paola
1999
Ergodic problems in differential games. Zbl 1153.91346
Alvarez, Olivier; Bardi, Martino
2007
Convergence by viscosity methods in multiscale financial models with stochastic volatility. Zbl 1189.35020
Bardi, Martino; Cesaroni, Annalisa; Manca, Luigi
2010
Discrete approximation of the minimal time function for systems with regular optimal trajectories. Zbl 0708.49012
Bardi, M.; Falcone, M.
1990
Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. I: Convex operators. Zbl 1135.35342
Bardi, Martino; Da Lio, Francesca
2001
Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations. Zbl 1158.91323
Bardi, Martino; Koike, Shigeaki; Soravia, Pierpaolo
2000
A geometric characterization of viable sets for controlled degenerate diffusions. Zbl 1031.93160
Bardi, Martino; Jensen, Robert
2002
Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. II: Concave operators. Zbl 1135.35343
Bardi, Martino; Da Lio, Francesca
2003
Fully discrete schemes for the value function of pursuit-evasion games. Zbl 0828.90147
Bardi, M.; Falcone, M.; Soravia, P.
1994
On differential games with long-time-average cost. Zbl 1188.49030
Bardi, Martino
2009
Convexity and semiconvexity along vector fields. Zbl 1232.26012
Bardi, Martino; Dragoni, Federica
2011
Uniqueness of solutions in mean field games with several populations and Neumann conditions. Zbl 1414.35107
Bardi, Martino; Cirant, Marco
2018
Comparison principles and Dirichlet problem for fully nonlinear degenerate equations of Monge-Ampére type. Zbl 1281.35056
Bardi, Martino; Mannucci, Paola
2013
A comparison result for Hamilton-Jacobi equations and applications to some differential games lacking controllability. Zbl 0823.49019
Bardi, Martino; Soravia, Pierpaolo
1994
New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs. Zbl 1426.35051
Bardi, Martino; Goffi, Alessandro
2019
An equation of growth of a single species with realistic dependence on crowding and seasonal factors. Zbl 0509.92021
Bardi, Martino
1983
A viscosity solutions approach to some asymptotic problems in optimal control. Zbl 0881.35013
Bagagiolo, F.; Bardi, M.; Capuzzo Dolcetta, I.
1997
The Bellman equation for time-optimal control of noncontrollable, nonlinear systems. Zbl 0797.49025
Bardi, Martino; Staicu, Vasile
1993
Optimal control with random parameters: a multiscale approach. Zbl 1248.49038
Bardi, Martino; Cesaroni, Annalisa
2011
Liouville properties and critical value of fully nonlinear elliptic operators. Zbl 1350.35045
Bardi, Martino; Cesaroni, Annalisa
2016
Hopf-type estimates and formulas for nonconvex nonconcave Hamilton-Jacobi equations. Zbl 0914.35026
Bardi, Martino; Faggian, Silvia
1998
Subdifferential and properties of convex functions with respect to vector fields. Zbl 1304.49033
Bardi, Martino; Dragoni, Federica
2014
Singular perturbation of a finite horizon problem with state-space constraints. Zbl 0953.49031
Bagagiolo, Fabio; Bardi, Martino
1998
Convergence of discrete schemes for discontinuous value functions of pursuit-evasion games. Zbl 0845.90140
Bardi, Martino; Bottacin, Sandra; Falcone, Maurizio
1995
Almost sure stabilizability of controlled degenerate diffusions. Zbl 1102.93040
Bardi, Martino; Cesaroni, Annalisa
2005
Preface: DGAA special issue on mean field games. Zbl 1304.00024
2013
Approximation of differential games of pursuit-evasion by discrete-time games. Zbl 0795.90098
Bardi, Martino; Soravia, Pierpaolo
1991
Large deviations for some fast stochastic volatility models by viscosity methods. Zbl 1332.93265
Bardi, Martino; Cesaroni, Annalisa; Ghilli, Daria
2015
On non-uniqueness and uniqueness of solutions in finite-horizon mean field games. Zbl 1437.91049
Bardi, Martino; Fischer, Markus
2019
On the homogenization of some non-coercive Hamilton-Jacobi-Isaacs equations. Zbl 1264.35019
Bardi, Martino; Terrone, Gabriele
2013
Comparison principles for subelliptic equations of Monge-Ampère type. Zbl 1203.35081
Bardi, Martino; Mannucci, Paola
2008
Convergence in multiscale financial models with non-Gaussian stochastic volatility. Zbl 1369.93713
Bardi, Martino; Cesaroni, Annalisa; Scotti, Andrea
2016
Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control. Zbl 1346.35067
Bardi, Martino; Cesaroni, Annalisa; Rossi, Luca
2016
Stochastic and differential games. Theory and numerical methods. Dedicated to Prof. A. I. Subbotin. Zbl 0919.00032
1999
An asymptotic formula for the Green’s function of an elliptic operator. Zbl 0672.35016
Bardi, Martino
1987
On the Dirichlet problem for nonlinear degenerate elliptic equations and applications to optimal control. Zbl 1027.49023
Bardi, M.; Bottacin, S.
1998
Some applications of viscosity solutions to optimal control and differential games. Zbl 0884.49020
Bardi, Martino
1997
Multiscale singular perturbations and homogenization of optimal control problems. Zbl 1206.93072
Alvarez, O.; Bardi, M.; Marchi, C.
2008
Comparison principles for equations of Monge-Ampère type in Carnot groups: a direct proof. Zbl 1187.35118
Bardi, Martino; Mannucci, Paola
2008
Exponential decay to stable states in phase transitions via a double log- transformation. Zbl 0732.34022
Bardi, Martino; Perthame, Benoit
1990
A PDE framework for games of pursuit-evasion type. Zbl 0679.90109
Bardi, Martino; Soravia, Pierpaolo
1989
Symmetry properties of solutions of Hamilton-Jacobi equations without uniqueness. Zbl 0736.35020
1990
A Dirichlet type problem for nonlinear degenerate elliptic equations arising in time-optimal stochastic control. Zbl 0970.35065
Bardi, Martino; Goatin, Paola; Ishii, Hitoshi
2000
Preface: DGAA 2nd special issue on mean field games. Zbl 1304.00025
2014
Convergence of some mean field games systems to aggregation and flocking models. Zbl 1460.35349
Bardi, Martino; Cardaliaguet, Pierre
2021
Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. Zbl 0968.49020
Bardi, Martino; Da Lio, Francesca
2000
Geometric properties of solutions of Hamilton-Jacobi equations. Zbl 0535.35005
Bardi, Martino
1985
Uniform estimates for some degenerating quasilinear elliptic equations and a bound on the Harnack constant for linear equations. Zbl 0735.35019
Bardi, Martino; Perthame, Benoît
1991
A Dijkstra-type algorithm for dynamic games. Zbl 1348.91060
Bardi, Martino; Maldonado López, Juan Pablo
2016
Cauchy problem and periodic homogenization for nonlocal Hamilton-Jacobi equations with coercive gradient terms. Zbl 1459.35020
Bardi, Martino; Cesaroni, Annalisa; Topp, Erwin
2020
Approximation and regular perturbation of optimal control problems via Hamilton-Jacobi theory. Zbl 0745.49024
Bardi, Martino; Sartori, Caterina
1991
Viscosity Lyapunov functions for almost sure stability of degenerate diffusions. Zbl 1057.34055
Bardi, Martino; Cesaroni, Annalisa
2002
Asymptotic symmetry of solutions of nonlinear partial differential equations. Zbl 0801.35015
1992
Homogenization of quasilinear elliptic equations with possibly superquadratic growth. Zbl 0831.35011
Bardi, M.
1995
Exchange of stability along a branch of periodic solutions of a single specie model. Zbl 0524.34047
Bardi, Martino
1983
Almost sure properties of controlled diffusions and worst case properties of deterministic systems. Zbl 1133.93036
Bardi, Martino; Cesaroni, Annalisa
2008
Right accessibility of semicontinuous initial data for Hamilton-Jacobi equations. Zbl 1053.35044
Bardi, Martino; Giga, Yoshikazu
2003
Convergence of some mean field games systems to aggregation and flocking models. Zbl 1460.35349
Bardi, Martino; Cardaliaguet, Pierre
2021
Cauchy problem and periodic homogenization for nonlocal Hamilton-Jacobi equations with coercive gradient terms. Zbl 1459.35020
Bardi, Martino; Cesaroni, Annalisa; Topp, Erwin
2020
New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs. Zbl 1426.35051
Bardi, Martino; Goffi, Alessandro
2019
On non-uniqueness and uniqueness of solutions in finite-horizon mean field games. Zbl 1437.91049
Bardi, Martino; Fischer, Markus
2019
Uniqueness of solutions in mean field games with several populations and Neumann conditions. Zbl 1414.35107
Bardi, Martino; Cirant, Marco
2018
Mean field games models of segregation. Zbl 1355.91003
Achdou, Yves; Bardi, Martino; Cirant, Marco
2017
Nonlinear elliptic systems and mean-field games. Zbl 1358.35198
Bardi, Martino; Feleqi, Ermal
2016
Liouville properties and critical value of fully nonlinear elliptic operators. Zbl 1350.35045
Bardi, Martino; Cesaroni, Annalisa
2016
Convergence in multiscale financial models with non-Gaussian stochastic volatility. Zbl 1369.93713
Bardi, Martino; Cesaroni, Annalisa; Scotti, Andrea
2016
Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control. Zbl 1346.35067
Bardi, Martino; Cesaroni, Annalisa; Rossi, Luca
2016
A Dijkstra-type algorithm for dynamic games. Zbl 1348.91060
Bardi, Martino; Maldonado López, Juan Pablo
2016
Large deviations for some fast stochastic volatility models by viscosity methods. Zbl 1332.93265
Bardi, Martino; Cesaroni, Annalisa; Ghilli, Daria
2015
Linear-quadratic $$N$$-person and mean-field games with ergodic cost. Zbl 1308.91008
Bardi, Martino; Priuli, Fabio S.
2014
Subdifferential and properties of convex functions with respect to vector fields. Zbl 1304.49033
Bardi, Martino; Dragoni, Federica
2014
Preface: DGAA 2nd special issue on mean field games. Zbl 1304.00025
2014
Comparison principles and Dirichlet problem for fully nonlinear degenerate equations of Monge-Ampére type. Zbl 1281.35056
Bardi, Martino; Mannucci, Paola
2013
Preface: DGAA special issue on mean field games. Zbl 1304.00024
2013
On the homogenization of some non-coercive Hamilton-Jacobi-Isaacs equations. Zbl 1264.35019
Bardi, Martino; Terrone, Gabriele
2013
Explicit solutions of some linear-quadratic mean field games. Zbl 1268.91017
Bardi, Martino
2012
Convexity and semiconvexity along vector fields. Zbl 1232.26012
Bardi, Martino; Dragoni, Federica
2011
Optimal control with random parameters: a multiscale approach. Zbl 1248.49038
Bardi, Martino; Cesaroni, Annalisa
2011
Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations. Zbl 1209.35001
Alvarez, Olivier; Bardi, Martino
2010
Convergence by viscosity methods in multiscale financial models with stochastic volatility. Zbl 1189.35020
Bardi, Martino; Cesaroni, Annalisa; Manca, Luigi
2010
On differential games with long-time-average cost. Zbl 1188.49030
Bardi, Martino
2009
Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Reprint of the 1997 original. Zbl 1134.49022
Bardi, Martino; Capuzzo-Dolcetta, Italo
2008
Comparison principles for subelliptic equations of Monge-Ampère type. Zbl 1203.35081
Bardi, Martino; Mannucci, Paola
2008
Multiscale singular perturbations and homogenization of optimal control problems. Zbl 1206.93072
Alvarez, O.; Bardi, M.; Marchi, C.
2008
Comparison principles for equations of Monge-Ampère type in Carnot groups: a direct proof. Zbl 1187.35118
Bardi, Martino; Mannucci, Paola
2008
Almost sure properties of controlled diffusions and worst case properties of deterministic systems. Zbl 1133.93036
Bardi, Martino; Cesaroni, Annalisa
2008
Multiscale problems and homogenization for second-order Hamilton-Jacobi equations. Zbl 1133.35005
Alvarez, Olivier; Bardi, Martino; Marchi, Claudio
2007
Ergodic problems in differential games. Zbl 1153.91346
Alvarez, Olivier; Bardi, Martino
2007
On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations. Zbl 1142.35041
Bardi, Martino; Mannucci, Paola
2006
Almost sure stabilizability of controlled degenerate diffusions. Zbl 1102.93040
Bardi, Martino; Cesaroni, Annalisa
2005
Singular perturbations of nonlinear degenerate parabolic pDEs: A general convergence result. Zbl 1032.35103
Alvarez, Olivier; Bardi, Martino
2003
Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. II: Concave operators. Zbl 1135.35343
Bardi, Martino; Da Lio, Francesca
2003
Right accessibility of semicontinuous initial data for Hamilton-Jacobi equations. Zbl 1053.35044
Bardi, Martino; Giga, Yoshikazu
2003
A geometric characterization of viable sets for controlled degenerate diffusions. Zbl 1031.93160
Bardi, Martino; Jensen, Robert
2002
Viscosity Lyapunov functions for almost sure stability of degenerate diffusions. Zbl 1057.34055
Bardi, Martino; Cesaroni, Annalisa
2002
Viscosity solutions methods for singular perturbations in deterministic and stochastic control. Zbl 1017.49028
Alvarez, Olivier; Bardi, Martino
2001
Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. I: Convex operators. Zbl 1135.35342
Bardi, Martino; Da Lio, Francesca
2001
Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations. Zbl 1158.91323
Bardi, Martino; Koike, Shigeaki; Soravia, Pierpaolo
2000
A Dirichlet type problem for nonlinear degenerate elliptic equations arising in time-optimal stochastic control. Zbl 0970.35065
Bardi, Martino; Goatin, Paola; Ishii, Hitoshi
2000
Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. Zbl 0968.49020
Bardi, Martino; Da Lio, Francesca
2000
On the strong maximum principle for fully nonlinear degenerate elliptic equations. Zbl 0939.35038
Bardi, Martino; Da Lio, Francesca
1999
Numerical methods for pursuit-evasion games via viscosity solutions. Zbl 1018.49027
Bardi, Martino; Falcone, Maurizio; Soravia, Pierpaolo
1999
Invariant sets for controlled degenerate diffusions: A viscosity solutions approach. Zbl 0928.93067
Bardi, Martino; Goatin, Paola
1999
Stochastic and differential games. Theory and numerical methods. Dedicated to Prof. A. I. Subbotin. Zbl 0919.00032
1999
Hopf-type estimates and formulas for nonconvex nonconcave Hamilton-Jacobi equations. Zbl 0914.35026
Bardi, Martino; Faggian, Silvia
1998
Singular perturbation of a finite horizon problem with state-space constraints. Zbl 0953.49031
Bagagiolo, Fabio; Bardi, Martino
1998
On the Dirichlet problem for nonlinear degenerate elliptic equations and applications to optimal control. Zbl 1027.49023
Bardi, M.; Bottacin, S.
1998
Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Zbl 0890.49011
Bardi, Martino; Capuzzo-Dolcetta, Italo
1997
On the Bellman equation for some unbounded control problems. Zbl 0894.49017
Bardi, Martino; Da Lio, Francesca
1997
A viscosity solutions approach to some asymptotic problems in optimal control. Zbl 0881.35013
Bagagiolo, F.; Bardi, M.; Capuzzo Dolcetta, I.
1997
Some applications of viscosity solutions to optimal control and differential games. Zbl 0884.49020
Bardi, Martino
1997
Convergence of discrete schemes for discontinuous value functions of pursuit-evasion games. Zbl 0845.90140
Bardi, Martino; Bottacin, Sandra; Falcone, Maurizio
1995
Homogenization of quasilinear elliptic equations with possibly superquadratic growth. Zbl 0831.35011
Bardi, M.
1995
Fully discrete schemes for the value function of pursuit-evasion games. Zbl 0828.90147
Bardi, M.; Falcone, M.; Soravia, P.
1994
A comparison result for Hamilton-Jacobi equations and applications to some differential games lacking controllability. Zbl 0823.49019
Bardi, Martino; Soravia, Pierpaolo
1994
The Bellman equation for time-optimal control of noncontrollable, nonlinear systems. Zbl 0797.49025
Bardi, Martino; Staicu, Vasile
1993
Asymptotic symmetry of solutions of nonlinear partial differential equations. Zbl 0801.35015
1992
The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations. Zbl 0733.35073
Bardi, Martino; Osher, Stanley
1991
Hamilton-Jacobi equations with singular boundary conditions on a free boundary and applications to differential games. Zbl 0732.35013
Bardi, Martino; Soravia, Pierpaolo
1991
Approximation of differential games of pursuit-evasion by discrete-time games. Zbl 0795.90098
Bardi, Martino; Soravia, Pierpaolo
1991
Uniform estimates for some degenerating quasilinear elliptic equations and a bound on the Harnack constant for linear equations. Zbl 0735.35019
Bardi, Martino; Perthame, Benoît
1991
Approximation and regular perturbation of optimal control problems via Hamilton-Jacobi theory. Zbl 0745.49024
Bardi, Martino; Sartori, Caterina
1991
An approximation scheme for the minimum time function. Zbl 0723.49024
Bardi, M; Falcone, M.
1990
Discrete approximation of the minimal time function for systems with regular optimal trajectories. Zbl 0708.49012
Bardi, M.; Falcone, M.
1990
Exponential decay to stable states in phase transitions via a double log- transformation. Zbl 0732.34022
Bardi, Martino; Perthame, Benoit
1990
Symmetry properties of solutions of Hamilton-Jacobi equations without uniqueness. Zbl 0736.35020
1990
A boundary value problem for the minimum-time function. Zbl 0682.49034
Bardi, Martino
1989
A PDE framework for games of pursuit-evasion type. Zbl 0679.90109
Bardi, Martino; Soravia, Pierpaolo
1989
An asymptotic formula for the Green’s function of an elliptic operator. Zbl 0672.35016
Bardi, Martino
1987
Geometric properties of solutions of Hamilton-Jacobi equations. Zbl 0535.35005
Bardi, Martino
1985
On Hopf’s formulas for solutions of Hamilton-Jacobi equations. Zbl 0569.35011
Bardi, M.; Evans, L. C.
1984
An equation of growth of a single species with realistic dependence on crowding and seasonal factors. Zbl 0509.92021
Bardi, Martino
1983
Exchange of stability along a branch of periodic solutions of a single specie model. Zbl 0524.34047
Bardi, Martino
1983
Predator-prey models in periodically fluctuating environments. Zbl 0466.92019
Bardi, Martino
1981
all top 5

### Cited by 1,339 Authors

 29 Camilli, Fabio 24 Bardi, Martino 20 Quincampoix, Marc 19 Barles, Guy 19 Cannarsa, Piermarco 19 Cardaliaguet, Pierre 18 Gomes, Diogo Luís Aguiar 18 Marchi, Claudio 18 Zidani, Hasnaa 15 Cesaroni, Annalisa 15 Ishii, Hitoshi 15 Serea, Oana-Silvia 14 Achdou, Yves 14 Siconolfi, Antonio 14 Tchou, Nicoletta Anna 13 Bokanowski, Olivier 13 Bressan, Alberto 13 Cirant, Marco 12 Falcone, Maurizio 12 Soravia, Pierpaolo 11 Davini, Andrea 11 Grüne, Lars 11 Mannucci, Paola 10 Barron, Emmanuel Nicholas 10 Gaitsgory, Vladimir G. 10 Kunisch, Karl 10 McEneaney, William “Mac” M. 9 Bagagiolo, Fabio 9 Da Lio, Francesca 9 Huang, Jianhui 9 Ley, Olivier 9 Liu, Qing 9 Silva, Francisco J. 9 Tran Vinh Hung 8 Bauso, Dario 8 Calder, Jeff 8 Capuzzo Dolcetta, Italo 8 Chen, Lansun 8 Crasta, Graziano 8 Festa, Adriano 8 Kumkov, Sergey S. 8 Lasry, Jean-Michel 8 Osher, Stanley Joel 8 Patsko, Valerii S. 8 Quaas, Alexander 7 Alla, Alessandro 7 Averboukh, Yuriĭ Vladimirovich 7 Bayraktar, Erhan 7 Dower, Peter M. 7 Frankowska, Hélène 7 Goffi, Alessandro 7 Goreac, Dan 7 Gozzi, Fausto 7 Hamamuki, Nao 7 Kalise, Dante 7 Lions, Pierre-Louis 7 Mitake, Hiroyoshi 7 Monneau, Régis 7 Nguyen, Khai T. 7 Świȩch, Andrzej 6 Bensoussan, Alain 6 Bettiol, Piernicola 6 Carlini, Elisabetta 6 Chasseigne, Emmanuel 6 Cristiani, Emiliano 6 Forcadel, Nicolas 6 Ghilli, Daria 6 Huang, Minyi 6 Jakobsen, Espen Robstad 6 Koike, Shigeaki 6 Kolokoltsov, Vassili N. 6 Kurzhanskiĭ, Aleksandr Borisovich 6 Marigonda, Antonio 6 Nour, Chadi 6 Perthame, Benoît 6 Sirakov, Boyan Slavchev 6 Souganidis, Panagiotis E. 6 Stern, Ronald Jay 6 Subbotina, Nina N. 6 Vinter, Richard B. 5 Albano, Paolo 5 Azcue, Pablo 5 Borkar, Vivek Shripad 5 Briani, Ariela 5 Clarke, Francis H. 5 Darbon, Jerome 5 Dragoni, Federica 5 Dykhta, Vladimir Aleksandrovich 5 Feleqi, Ermal 5 Felmer, Patricio L. 5 Ferretti, Roberto Giorgio 5 Fujita, Yasuhiro 5 Giga, Yoshikazu 5 Jensen, Robert R. 5 Kraaij, Richard Clemens 5 Malusa, Annalisa 5 Mirebeau, Jean-Marie 5 Misztela, Arkadiusz 5 Motta, Monica 5 Muler, Nora E. ...and 1,239 more Authors
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### Cited in 254 Serials

 61 Journal of Differential Equations 53 Applied Mathematics and Optimization 51 SIAM Journal on Control and Optimization 51 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 51 Dynamic Games and Applications 41 Journal of Optimization Theory and Applications 41 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 35 Calculus of Variations and Partial Differential Equations 33 Journal of Mathematical Analysis and Applications 27 NoDEA. Nonlinear Differential Equations and Applications 24 Automatica 21 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 20 Systems & Control Letters 18 Transactions of the American Mathematical Society 18 Journal of Scientific Computing 16 Journal of Computational Physics 16 Communications in Partial Differential Equations 16 Journal de Mathématiques Pures et Appliquées. Neuvième Série 15 Archive for Rational Mechanics and Analysis 13 Discrete and Continuous Dynamical Systems 12 SIAM Journal on Mathematical Analysis 12 Communications on Pure and Applied Analysis 12 Journal of Dynamics and Games 11 Automation and Remote Control 9 Journal of Functional Analysis 9 Discrete and Continuous Dynamical Systems. Series B 9 Minimax Theory and its Applications 8 Applied Mathematics and Computation 8 Applied Numerical Mathematics 8 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 8 Stochastic Processes and their Applications 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 Chaos, Solitons and Fractals 7 MCSS. Mathematics of Control, Signals, and Systems 7 The Annals of Applied Probability 7 Journal of Global Optimization 7 Proceedings of the Steklov Institute of Mathematics 7 Discrete and Continuous Dynamical Systems. Series S 7 Mathematical Control and Related Fields 6 Mathematics of Computation 6 Numerische Mathematik 6 SIAM Journal on Scientific Computing 6 Journal of Mathematical Sciences (New York) 6 European Journal of Control 6 Journal of the European Mathematical Society (JEMS) 6 Set-Valued and Variational Analysis 6 Nonlinear Analysis. Theory, Methods & Applications 5 International Journal of Control 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Journal of Computational and Applied Mathematics 5 Mathematische Annalen 5 SIAM Journal on Numerical Analysis 5 Optimal Control Applications & Methods 5 Insurance Mathematics & Economics 5 SIAM Journal on Applied Mathematics 5 International Journal of Robust and Nonlinear Control 5 Journal of Convex Analysis 5 Differential Equations 5 Nonlinear Analysis. Real World Applications 4 Communications on Pure and Applied Mathematics 4 Journal of Mathematical Biology 4 Nonlinearity 4 Prikladnaya Matematika i Mekhanika 4 International Journal of Game Theory 4 International Journal of Adaptive Control and Signal Processing 4 The Journal of Geometric Analysis 4 Journal of Dynamics and Differential Equations 4 Doklady Mathematics 4 Networks and Heterogeneous Media 4 Research in the Mathematical Sciences 4 Mathematics in Engineering 3 Applicable Analysis 3 Computers & Mathematics with Applications 3 Journal of Applied Mathematics and Mechanics 3 Journal of Statistical Physics 3 Mathematical Biosciences 3 Advances in Mathematics 3 Journal of Mathematical Economics 3 Mathematics of Operations Research 3 Proceedings of the American Mathematical Society 3 Chinese Annals of Mathematics. Series B 3 Acta Applicandae Mathematicae 3 Journal of Economic Dynamics & Control 3 Mathematical and Computer Modelling 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Journal of Mathematical Imaging and Vision 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Computational Optimization and Applications 3 Computational and Applied Mathematics 3 Mathematical Finance 3 Abstract and Applied Analysis 3 Communications in Contemporary Mathematics 3 Journal of Evolution Equations 3 Journal of Systems Science and Complexity 3 SIAM Journal on Applied Dynamical Systems 3 Nonlinear Analysis. Hybrid Systems 3 SIAM Journal on Imaging Sciences 3 Journal of Computational Dynamics 3 SN Partial Differential Equations and Applications ...and 154 more Serials
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### Cited in 39 Fields

 695 Calculus of variations and optimal control; optimization (49-XX) 560 Partial differential equations (35-XX) 317 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 299 Systems theory; control (93-XX) 154 Numerical analysis (65-XX) 127 Probability theory and stochastic processes (60-XX) 99 Operations research, mathematical programming (90-XX) 87 Ordinary differential equations (34-XX) 65 Biology and other natural sciences (92-XX) 63 Dynamical systems and ergodic theory (37-XX) 37 Mechanics of particles and systems (70-XX) 30 Real functions (26-XX) 25 Operator theory (47-XX) 20 Computer science (68-XX) 18 Differential geometry (53-XX) 17 Statistical mechanics, structure of matter (82-XX) 16 Global analysis, analysis on manifolds (58-XX) 12 Mechanics of deformable solids (74-XX) 11 Integral equations (45-XX) 9 Statistics (62-XX) 8 Fluid mechanics (76-XX) 8 Optics, electromagnetic theory (78-XX) 7 Functional analysis (46-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Convex and discrete geometry (52-XX) 4 General and overarching topics; collections (00-XX) 4 Topological groups, Lie groups (22-XX) 4 Measure and integration (28-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Information and communication theory, circuits (94-XX) 3 Combinatorics (05-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Difference and functional equations (39-XX) 3 Quantum theory (81-XX) 3 Geophysics (86-XX) 2 Functions of a complex variable (30-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Relativity and gravitational theory (83-XX)