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Limit of the infinite horizon discounted Hamilton-Jacobi equation
1. | CIMAT, A.P. 402, 3600, Guanajuato. Gto |
2. | I. de Matemáticas, UNAM, Cd. Universitaria, México, D.F. 04510 |
References:
[1] |
N. Anantharaman, R. Iturriaga, P. Padilla and H. Sánchez-Morgado, Physical solutions of the Hamilton-Jacobi equation,, Disc. Cont. Dyn. Sys. Series B, 5 (2005), 513.
doi: 10.3934/dcdsb.2005.5.513. |
[2] |
M. Bardi and I. C. Dolcetta, "Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations,", Birkhausser, (1997).
doi: 10.1007/978-0-8176-4755-1. |
[3] |
G. Barles, "Solutions de Viscosité des Équations de Hamilton Jacobi,", Mathématiques et Applications, 17 (1994).
|
[4] |
P. Bernard, Existence of $C^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds,, Ann. Scient. Éc. Norm. Sup., 40 (2007), 445.
|
[5] |
G. Contreras, Action Potential and Weak KAM Solutions,, Calc. Var. Partial Differential Equations, 13 (2001), 427.
doi: 10.1007/s005260100081. |
[6] |
G. Contreras and R. Iturriaga, "Global Minimizers of Autonomous Lagrangians,", 22 Colóquio Brasileiro de Matemática, (1999).
|
[7] |
A. Fathi, "The Weak KAM Theorem in Lagrangian Dynamics,", Cambridge Studies in Advanced Mathematics, (2010). Google Scholar |
[8] |
A. Fathi, Solutions KAM faibles conjuguées et barrières de Peierls,, C. R. Acad. Sci. Paris, 325 (1997), 649.
|
[9] |
A. Fathi, Théorème KAM faible et Théorie de Mather sur les systems Lagrangiens,, C.R. Acad. Sci. Paris, 324 (1997), 1043.
|
[10] |
A. Fathi, Sur la convergence du semi-groupe de Lax-Oleinik,, C. R. Acad. Sci. Paris, 327 (1998), 267.
|
[11] |
A. Fathi and A. Siconolfi, Existence of $C^1$ critical subsolutions of the Hamilton Jacobi equation,, Invent. Math., 155 (2004), 363.
doi: 10.1007/s00222-003-0323-6. |
[12] |
D. Gomes, Generalized Mather problem and selection principles for viscosity solutions and Mather measures,, Advances in Calculus of Variations, 1 (2008), 291.
doi: 10.1515/ACV.2008.012. |
[13] |
R. Mañé, Lagrangian flows: The dynamics of globally minimizing orbits,, in, 362 (1996), 120.
doi: 10.1007/BF01233389. |
[14] |
J. Mather, Action minimizing measures for positive definite Lagrangian systems,, Math. Z., 207 (1991), 169.
doi: 10.1007/BF02571383. |
show all references
References:
[1] |
N. Anantharaman, R. Iturriaga, P. Padilla and H. Sánchez-Morgado, Physical solutions of the Hamilton-Jacobi equation,, Disc. Cont. Dyn. Sys. Series B, 5 (2005), 513.
doi: 10.3934/dcdsb.2005.5.513. |
[2] |
M. Bardi and I. C. Dolcetta, "Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations,", Birkhausser, (1997).
doi: 10.1007/978-0-8176-4755-1. |
[3] |
G. Barles, "Solutions de Viscosité des Équations de Hamilton Jacobi,", Mathématiques et Applications, 17 (1994).
|
[4] |
P. Bernard, Existence of $C^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds,, Ann. Scient. Éc. Norm. Sup., 40 (2007), 445.
|
[5] |
G. Contreras, Action Potential and Weak KAM Solutions,, Calc. Var. Partial Differential Equations, 13 (2001), 427.
doi: 10.1007/s005260100081. |
[6] |
G. Contreras and R. Iturriaga, "Global Minimizers of Autonomous Lagrangians,", 22 Colóquio Brasileiro de Matemática, (1999).
|
[7] |
A. Fathi, "The Weak KAM Theorem in Lagrangian Dynamics,", Cambridge Studies in Advanced Mathematics, (2010). Google Scholar |
[8] |
A. Fathi, Solutions KAM faibles conjuguées et barrières de Peierls,, C. R. Acad. Sci. Paris, 325 (1997), 649.
|
[9] |
A. Fathi, Théorème KAM faible et Théorie de Mather sur les systems Lagrangiens,, C.R. Acad. Sci. Paris, 324 (1997), 1043.
|
[10] |
A. Fathi, Sur la convergence du semi-groupe de Lax-Oleinik,, C. R. Acad. Sci. Paris, 327 (1998), 267.
|
[11] |
A. Fathi and A. Siconolfi, Existence of $C^1$ critical subsolutions of the Hamilton Jacobi equation,, Invent. Math., 155 (2004), 363.
doi: 10.1007/s00222-003-0323-6. |
[12] |
D. Gomes, Generalized Mather problem and selection principles for viscosity solutions and Mather measures,, Advances in Calculus of Variations, 1 (2008), 291.
doi: 10.1515/ACV.2008.012. |
[13] |
R. Mañé, Lagrangian flows: The dynamics of globally minimizing orbits,, in, 362 (1996), 120.
doi: 10.1007/BF01233389. |
[14] |
J. Mather, Action minimizing measures for positive definite Lagrangian systems,, Math. Z., 207 (1991), 169.
doi: 10.1007/BF02571383. |
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