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Chinese Annals of Mathematics, Series B, ISSN 0252-9599, 3/2017, Volume 38, Issue 2, pp. 379 - 392
This paper records for the Hamiltonian H = 1/2 |p|2 + W(x) some old and new identities relevant for the PDE/variational approach to weak KAM theory. 
35A15 | Effective Hamiltonian | Mathematics, general | Weak KAM theory | Mathematics | 37J40 | Applications of Mathematics | Hamiltonian dynamics | MATHEMATICS | PDE METHODS | LAGRANGIAN SYSTEMS
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 11/2016, Volume 36, Issue 11, pp. 6167 - 6185
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 267, Issue 4, pp. 2448 - 2470
For mechanical Hamiltonian systems on the torus, we study the dynamical properties of the generalized characteristic semiflows associated with the... 
Generalized characteristic | Weak KAM theory | Hamilton-Jacobi equation | Singularities | TOTAL DISCONNECTEDNESS | MATHEMATICS | VISCOSITY SOLUTIONS | SET | HOMOCLINIC ORBITS | LASRY-LIONS
Journal Article
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 01/2013, Volume 18, Issue 1, pp. 57 - 94
.... This is equivalent to the solvability of an associated multi-time Hamilton-Jacobi equation. We examine the weak KAM theoretic aspects of the commutation property and show... 
Multi-time Hamilton-Jacobi equation | Commuting Hamiltonians | Weak KAM theory | Aubry-Mather theory | Viscosity solutions | multi-time Hamilton-Jacobi equation | MATHEMATICS, APPLIED | weak KAM theory | JACOBI EQUATIONS | MATHER THEORY | CONVEX HAMILTONIANS | MULTITIME EQUATIONS | CONTINUITY | REGULARITY | LARGE TIME BEHAVIOR | SYSTEMS | MANIFOLDS | viscosity solutions
Journal Article
Minimax Theory and its Applications, ISSN 2199-1413, 2018, Volume 3, Issue 2, pp. 313 - 322
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2012, Volume 87, Issue 1, pp. 1 - 39
In this paper, we explain some facts on the discrete case of weak KAM theory. In that setting, the Lagrangian is replaced by a cost $c\colon X\times X \rightarrow \mathbb{R}$, on a “reasonable” space $X... 
Partial differential equations | General | Dynamical systems and ergodic theory | MATHEMATICS | SUBSOLUTIONS | MANIFOLDS | Discrete weak KAM theory | Aubry-Mather theory | continuous and discontinuous critical sub-solutions
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 04/2013, Volume 15, Issue 2, pp. 1250055 - 1250036
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2012, Volume 87, Issue 1, pp. 1 - 39
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 2011, Volume 95, Issue 1, pp. 99 - 135
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 2013, Volume 13, Issue 4, pp. 853 - 866
This paper contributes several results on weak KAM theory for time-periodic Tonelli Lagrangian systems. Wang and Yan [Commun. Math. Phys. 309 (2012), 663-691... 
New Lax-Oleinik type operators | Hamilton-Jacobi equations | Weak KAM theory | Time-periodic Tonelli Lagrangians | LAX-OLEINIK SEMIGROUP | MATHEMATICS | MATHEMATICS, APPLIED | time-periodic Tonelli Lagrangians | PSEUDOGRAPHS | ORBITS | CONVERGENCE | weak KAM theory | new Lax-Oleinik type operators
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 06/2015, Volume 280, Issue 1-2, pp. 165 - 194
Journal Article
Dynamic games and applications, ISSN 2153-0793, 2019, Volume 10, Issue 2, pp. 361 - 390
The aim of this paper is to study the long-time behavior of solutions to deterministic mean field games systems on Euclidean space. This problem was addressed... 
Weak KAM theory | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | WEAK KAM THEOREM | Mean field games | Long-time behavior | Viscosity solutions | Mathematics - Optimization and Control
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 09/2020, Volume 269, Issue 7, pp. 5730 - 5753
We investigated several global behaviors of the weak KAM solutions uc(x,t) parametrized by c∈H1(T,R). For the suspended Hamiltonian H... 
Exact syplectic twist map | Aubry Mather theory | Hamilton Jacobi equation | Generalized characteristics | Transition chain | Weak KAM solution
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 11/2016, Volume 36, Issue 11, pp. 6487 - 6522
.... By introducing an implicitly defined solution semigroup and an admissible value set C-H, we extend weak KAM theory to certain more general cases, in which H depends on the unknown function u explicitly... 
Hamilton-Jacobi equations | Weak KAM theory | Viscosity solutions | LAX-OLEINIK SEMIGROUP | MATHEMATICS | MATHEMATICS, APPLIED | DEFINITE LAGRANGIAN SYSTEMS | LONG-TIME BEHAVIOR | CONVERGENCE | FRENKEL-KONTOROVA MODEL | viscosity solutions
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2016, Volume 85, Issue 297, pp. 85 - 117
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2018, Volume 265, Issue 2, pp. 719 - 732
We study the Lasry–Lions approximation using the kernel determined by the fundamental solution with respect to a time-dependent Tonelli Lagrangian. This... 
Aubry–Mather theory | Weak KAM theory | Hamilton–Jacobi equations | Lasry–Lions regularization | MATHEMATICS | Hamilton-Jacobi equations | HILBERT-SPACES | SET | LAX-OLEINIK | LEMMA | POINT-OF-VIEW | DYNAMICS | Lasry-Lions regularization | Aubry-Mather theory | REGULARIZATION
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 03/2016, Volume 33, Issue 2, pp. 243 - 272
We prove that any continuous and convex stationary ergodic Hamiltonian admits critical subsolutions, which are strict outside the random Aubry set. They make... 
Homogenization | Weak KAM Theory | Stationary ergodic setting | Viscosity solutions | WEAK KAM | MATHEMATICS, APPLIED | BOLZA PROBLEMS | HAMILTON-JACOBI EQUATIONS | MANIFOLDS | DISCONTINUOUS LAGRANGIANS
Journal Article
Dynamic games and applications, ISSN 2153-0793, 2016, Volume 7, Issue 4, pp. 657 - 682
Journal Article
Journal of the American Mathematical Society, ISSN 0894-0347, 09/2008, Volume 21, Issue 3, pp. 615 - 669
Journal Article
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