-
Previous Article
Infinite translation surfaces with infinitely generated Veech groups
- JMD Home
- This Issue
-
Next Article
Structure of attractors for $(a,b)$-continued fraction transformations
Existence of $C^{1,1}$ critical subsolutions in discrete weak KAM theory
1. | Unité de Mathématiques Pures et Appliquées, École Normale Supérieure de Lyon, siteMonod, UMR CNRS 5669, 46, allée d’Italie, 69364 LYON Cedex 07, France |
References:
[1] |
V. Bangert, Mather sets for twist maps and geodesics on tori, "Dynamics reported, Vol. 1,", 1-56, (1988), 1.
|
[2] |
Patrick Bernard and Boris Buffoni, The Monge problem for supercritical Mañé potentials on compact manifolds,, Adv. Math., 207 (2006), 691.
doi: 10.1016/j.aim.2006.01.003. |
[3] |
Patrick Bernard and Boris Buffoni, Optimal mass transportation and Mather theory,, J. Eur. Math. Soc. (JEMS), 9 (2007), 85.
doi: 10.4171/JEMS/74. |
[4] |
Patrick Bernard and Boris Buffoni, Weak KAM pairs and Monge-Kantorovich duality, "Asymptotic Analysis and Singularities-Elliptic and Parabolic PDEs and Related Problems,", 397-420, (2007), 397.
|
[5] |
Patrick Bernard, Existence of $C^{1,1}$ critical subsolutions of the Hamilton-Jacobi equation on compact manifolds,, Ann. Sci. École Norm. Sup. (4), 40 (2007), 445.
|
[6] |
Patrick Bernard, The dynamics of pseudographs in convex Hamiltonian systems,, J. Amer. Math. Soc., 21 (2008), 615.
doi: 10.1090/S0894-0347-08-00591-2. |
[7] |
Patrick Bernard, Lasry-Lions regularisation and a Lemma of Ilmanen,, to appear in Rendiconti del Seminario Matematico della Università di Padova., (). Google Scholar |
[8] |
Patrick Bernard, Personal communication,, 2009., (). Google Scholar |
[9] |
Pierre Cardaliaguet, Front propagation problems with nonlocal terms. II,, J. Math. Anal. Appl., 260 (2001), 572.
doi: 10.1006/jmaa.2001.7483. |
[10] |
Guillaume Carlier, Duality and existence for a class of mass transportation problems and economic applications, "Advances in mathematical economics. Vol. 5,", 1-21, (2003), 1.
|
[11] |
Gonzalo Contreras, Renato Iturriaga and Hector Sanchez-Morgado, Weak solutions of the Hamilton-Jacobi equation for time periodic Lagrangians,, preprint, (2000). Google Scholar |
[12] |
F. H. Clarke, Y. S. Ledyaev, R. J. Stern and P. R. Wolenski, "Nonsmooth Analysis and Control Theory," volume 178 of "Graduate Texts in Mathematics,", Springer-Verlag, (1998).
|
[13] |
Piermarco Cannarsa and Carlo Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control,", Progress in Nonlinear Differential Equations and their Applications, (2004).
|
[14] |
Albert Fathi, "Weak KAM Theorem in Lagrangian Dynamics,", preliminary version. , (). Google Scholar |
[15] |
Albert Fathi, Personal communication,, 2009., (). Google Scholar |
[16] |
Albert Fathi and Alessio Figalli, Optimal transportation on noncompact manifolds,, Israel J. Math., 175 (2010), 1.
doi: 10.1007/s11856-010-0001-5. |
[17] |
Albert Fathi, Alessio Figalli and Ludovic Rifford, On the Hausdorff dimension of the Mather quotient,, Comm. Pure Appl. Math., 62 (2009), 445.
doi: 10.1002/cpa.20250. |
[18] |
A. Fathi and E. Maderna, Weak KAM Theorem on noncompact manifolds,, NoDEA, 14 (2007), 1.
doi: 10.1007/s00030-007-2047-6. |
[19] |
Albert Fathi and Antonio Siconolfi, Existence of $C^1$ critical subsolutions of the Hamilton-Jacobi equation,, Invent. Math., 155 (2004), 363.
doi: 10.1007/s00222-003-0323-6. |
[20] |
Albert Fathi and Maxime Zavidovique, Insertion of $C^{1,1}$ functions and Ilmanen's lemma,, to appear in Rendiconti del Seminario Matematico della Università di Padova., (). Google Scholar |
[21] |
Christophe Golé, "Symplectic Twist Maps,", Global variational techniques. Advanced Series in Nonlinear Dynamics, (2001).
|
[22] |
Michael-R. Herman, Inégalités "a priori'' pour des tores lagrangiens invariants par des difféomorphismes symplectiques,, Inst. Hautes Études Sci. Publ. Math. No. 70, (1989), 47.
|
[23] |
Tom Ilmanen, "The Level-Set Flow on a Manifold," "Differential Geometry: Partial Differential Equations on Manifolds (Los Angeles, CA, 1990),", 193-204, (1993), 193.
|
[24] |
Daniel Massart, Subsolutions of time-periodic Hamilton-Jacobi equations,, Ergodic Theory Dynam. Systems, 27 (2007), 1253.
doi: 10.1017/S0143385707000089. |
[25] |
John Mather, A criterion for the nonexistence of invariant circles,, Inst. Hautes Études Sci. Publ. Math. No. 63, (1986), 153.
|
[26] |
John N. Mather, Action minimizing invariant measures for positive-definite Lagrangian systems,, Math. Z., 207 (1991), 169.
doi: 10.1007/BF02571383. |
[27] |
John N. Mather, Variational construction of connecting orbits,, Ann. Inst. Fourier (Grenoble), 43 (1993), 1349.
|
[28] |
John N. Mather and Giovanni Forni, Action minimizing orbits in Hamiltonian systems, "Transition to chaos in classical and quantum mechanics (Montecatini Terme, 1991),", 92-186, (1589), 92.
|
[29] |
Maxime Zavidovique, Strict subsolutions and Mañe potential in discrete weak KAM theory,, to appear in Commentarii Mathematici Helvetici., (). Google Scholar |
show all references
References:
[1] |
V. Bangert, Mather sets for twist maps and geodesics on tori, "Dynamics reported, Vol. 1,", 1-56, (1988), 1.
|
[2] |
Patrick Bernard and Boris Buffoni, The Monge problem for supercritical Mañé potentials on compact manifolds,, Adv. Math., 207 (2006), 691.
doi: 10.1016/j.aim.2006.01.003. |
[3] |
Patrick Bernard and Boris Buffoni, Optimal mass transportation and Mather theory,, J. Eur. Math. Soc. (JEMS), 9 (2007), 85.
doi: 10.4171/JEMS/74. |
[4] |
Patrick Bernard and Boris Buffoni, Weak KAM pairs and Monge-Kantorovich duality, "Asymptotic Analysis and Singularities-Elliptic and Parabolic PDEs and Related Problems,", 397-420, (2007), 397.
|
[5] |
Patrick Bernard, Existence of $C^{1,1}$ critical subsolutions of the Hamilton-Jacobi equation on compact manifolds,, Ann. Sci. École Norm. Sup. (4), 40 (2007), 445.
|
[6] |
Patrick Bernard, The dynamics of pseudographs in convex Hamiltonian systems,, J. Amer. Math. Soc., 21 (2008), 615.
doi: 10.1090/S0894-0347-08-00591-2. |
[7] |
Patrick Bernard, Lasry-Lions regularisation and a Lemma of Ilmanen,, to appear in Rendiconti del Seminario Matematico della Università di Padova., (). Google Scholar |
[8] |
Patrick Bernard, Personal communication,, 2009., (). Google Scholar |
[9] |
Pierre Cardaliaguet, Front propagation problems with nonlocal terms. II,, J. Math. Anal. Appl., 260 (2001), 572.
doi: 10.1006/jmaa.2001.7483. |
[10] |
Guillaume Carlier, Duality and existence for a class of mass transportation problems and economic applications, "Advances in mathematical economics. Vol. 5,", 1-21, (2003), 1.
|
[11] |
Gonzalo Contreras, Renato Iturriaga and Hector Sanchez-Morgado, Weak solutions of the Hamilton-Jacobi equation for time periodic Lagrangians,, preprint, (2000). Google Scholar |
[12] |
F. H. Clarke, Y. S. Ledyaev, R. J. Stern and P. R. Wolenski, "Nonsmooth Analysis and Control Theory," volume 178 of "Graduate Texts in Mathematics,", Springer-Verlag, (1998).
|
[13] |
Piermarco Cannarsa and Carlo Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control,", Progress in Nonlinear Differential Equations and their Applications, (2004).
|
[14] |
Albert Fathi, "Weak KAM Theorem in Lagrangian Dynamics,", preliminary version. , (). Google Scholar |
[15] |
Albert Fathi, Personal communication,, 2009., (). Google Scholar |
[16] |
Albert Fathi and Alessio Figalli, Optimal transportation on noncompact manifolds,, Israel J. Math., 175 (2010), 1.
doi: 10.1007/s11856-010-0001-5. |
[17] |
Albert Fathi, Alessio Figalli and Ludovic Rifford, On the Hausdorff dimension of the Mather quotient,, Comm. Pure Appl. Math., 62 (2009), 445.
doi: 10.1002/cpa.20250. |
[18] |
A. Fathi and E. Maderna, Weak KAM Theorem on noncompact manifolds,, NoDEA, 14 (2007), 1.
doi: 10.1007/s00030-007-2047-6. |
[19] |
Albert Fathi and Antonio Siconolfi, Existence of $C^1$ critical subsolutions of the Hamilton-Jacobi equation,, Invent. Math., 155 (2004), 363.
doi: 10.1007/s00222-003-0323-6. |
[20] |
Albert Fathi and Maxime Zavidovique, Insertion of $C^{1,1}$ functions and Ilmanen's lemma,, to appear in Rendiconti del Seminario Matematico della Università di Padova., (). Google Scholar |
[21] |
Christophe Golé, "Symplectic Twist Maps,", Global variational techniques. Advanced Series in Nonlinear Dynamics, (2001).
|
[22] |
Michael-R. Herman, Inégalités "a priori'' pour des tores lagrangiens invariants par des difféomorphismes symplectiques,, Inst. Hautes Études Sci. Publ. Math. No. 70, (1989), 47.
|
[23] |
Tom Ilmanen, "The Level-Set Flow on a Manifold," "Differential Geometry: Partial Differential Equations on Manifolds (Los Angeles, CA, 1990),", 193-204, (1993), 193.
|
[24] |
Daniel Massart, Subsolutions of time-periodic Hamilton-Jacobi equations,, Ergodic Theory Dynam. Systems, 27 (2007), 1253.
doi: 10.1017/S0143385707000089. |
[25] |
John Mather, A criterion for the nonexistence of invariant circles,, Inst. Hautes Études Sci. Publ. Math. No. 63, (1986), 153.
|
[26] |
John N. Mather, Action minimizing invariant measures for positive-definite Lagrangian systems,, Math. Z., 207 (1991), 169.
doi: 10.1007/BF02571383. |
[27] |
John N. Mather, Variational construction of connecting orbits,, Ann. Inst. Fourier (Grenoble), 43 (1993), 1349.
|
[28] |
John N. Mather and Giovanni Forni, Action minimizing orbits in Hamiltonian systems, "Transition to chaos in classical and quantum mechanics (Montecatini Terme, 1991),", 92-186, (1589), 92.
|
[29] |
Maxime Zavidovique, Strict subsolutions and Mañe potential in discrete weak KAM theory,, to appear in Commentarii Mathematici Helvetici., (). Google Scholar |
[1] |
Yuri Chekanov, Felix Schlenk. Notes on monotone Lagrangian twist tori. Electronic Research Announcements, 2010, 17: 104-121. doi: 10.3934/era.2010.17.104 |
[2] |
Z. Reichstein and B. Youssin. Parusinski's "Key Lemma" via algebraic geometry. Electronic Research Announcements, 1999, 5: 136-145. |
[3] |
Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311 |
[4] |
Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1717-1746. doi: 10.3934/dcdss.2020451 |
[5] |
M. R. S. Kulenović, J. Marcotte, O. Merino. Properties of basins of attraction for planar discrete cooperative maps. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2721-2737. doi: 10.3934/dcdsb.2020202 |
[6] |
W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349 |
[7] |
Ronald E. Mickens. Positivity preserving discrete model for the coupled ODE's modeling glycolysis. Conference Publications, 2003, 2003 (Special) : 623-629. doi: 10.3934/proc.2003.2003.623 |
[8] |
John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021 doi: 10.3934/jdg.2021004 |
[9] |
Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183 |
[10] |
Jan Prüss, Laurent Pujo-Menjouet, G.F. Webb, Rico Zacher. Analysis of a model for the dynamics of prions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 225-235. doi: 10.3934/dcdsb.2006.6.225 |
[11] |
Simone Calogero, Juan Calvo, Óscar Sánchez, Juan Soler. Dispersive behavior in galactic dynamics. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 1-16. doi: 10.3934/dcdsb.2010.14.1 |
[12] |
Carlos Gutierrez, Nguyen Van Chau. A remark on an eigenvalue condition for the global injectivity of differentiable maps of $R^2$. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 397-402. doi: 10.3934/dcds.2007.17.397 |
[13] |
Francisco Braun, Jaume Llibre, Ana Cristina Mereu. Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5245-5255. doi: 10.3934/dcds.2016029 |
[14] |
Fernando P. da Costa, João T. Pinto, Rafael Sasportes. On the convergence to critical scaling profiles in submonolayer deposition models. Kinetic & Related Models, 2018, 11 (6) : 1359-1376. doi: 10.3934/krm.2018053 |
[15] |
Gioconda Moscariello, Antonia Passarelli di Napoli, Carlo Sbordone. Planar ACL-homeomorphisms : Critical points of their components. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1391-1397. doi: 10.3934/cpaa.2010.9.1391 |
[16] |
Chin-Chin Wu. Existence of traveling wavefront for discrete bistable competition model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 973-984. doi: 10.3934/dcdsb.2011.16.973 |
[17] |
Ian Schindler, Kyril Tintarev. Mountain pass solutions to semilinear problems with critical nonlinearity. Conference Publications, 2007, 2007 (Special) : 912-919. doi: 10.3934/proc.2007.2007.912 |
[18] |
Matthias Erbar, Jan Maas. Gradient flow structures for discrete porous medium equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1355-1374. doi: 10.3934/dcds.2014.34.1355 |
[19] |
Juan Manuel Pastor, Javier García-Algarra, Javier Galeano, José María Iriondo, José J. Ramasco. A simple and bounded model of population dynamics for mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 53-70. doi: 10.3934/nhm.2015.10.53 |
[20] |
Marian Gidea, Rafael de la Llave, Tere M. Seara. A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold. Discrete & Continuous Dynamical Systems - A, 2020, 40 (12) : 6795-6813. doi: 10.3934/dcds.2020166 |
2019 Impact Factor: 0.465
Tools
Metrics
Other articles
by authors
[Back to Top]