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Minimax and viscosity solutions of Hamilton-Jacobi equations in the convex case
1. | Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7 - 35131 Padova, Italy, Italy |
[1] |
Mihai Bostan, Gawtum Namah. Time periodic viscosity solutions of Hamilton-Jacobi equations. Communications on Pure & Applied Analysis, 2007, 6 (2) : 389-410. doi: 10.3934/cpaa.2007.6.389 |
[2] |
Kaizhi Wang, Jun Yan. Lipschitz dependence of viscosity solutions of Hamilton-Jacobi equations with respect to the parameter. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1649-1659. doi: 10.3934/dcds.2016.36.1649 |
[3] |
Manuel de León, David Martín de Diego, Miguel Vaquero. A Hamilton-Jacobi theory on Poisson manifolds. Journal of Geometric Mechanics, 2014, 6 (1) : 121-140. doi: 10.3934/jgm.2014.6.121 |
[4] |
Kai Zhao, Wei Cheng. On the vanishing contact structure for viscosity solutions of contact type Hamilton-Jacobi equations I: Cauchy problem. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4345-4358. doi: 10.3934/dcds.2019176 |
[5] |
Nalini Anantharaman, Renato Iturriaga, Pablo Padilla, Héctor Sánchez-Morgado. Physical solutions of the Hamilton-Jacobi equation. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 513-528. doi: 10.3934/dcdsb.2005.5.513 |
[6] |
Giuseppe Marmo, Giuseppe Morandi, Narasimhaiengar Mukunda. The Hamilton-Jacobi theory and the analogy between classical and quantum mechanics. Journal of Geometric Mechanics, 2009, 1 (3) : 317-355. doi: 10.3934/jgm.2009.1.317 |
[7] |
Yasuhiro Fujita, Katsushi Ohmori. Inequalities and the Aubry-Mather theory of Hamilton-Jacobi equations. Communications on Pure & Applied Analysis, 2009, 8 (2) : 683-688. doi: 10.3934/cpaa.2009.8.683 |
[8] |
Melvin Leok, Diana Sosa. Dirac structures and Hamilton-Jacobi theory for Lagrangian mechanics on Lie algebroids. Journal of Geometric Mechanics, 2012, 4 (4) : 421-442. doi: 10.3934/jgm.2012.4.421 |
[9] |
Xifeng Su, Lin Wang, Jun Yan. Weak KAM theory for HAMILTON-JACOBI equations depending on unknown functions. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6487-6522. doi: 10.3934/dcds.2016080 |
[10] |
Olga Bernardi, Franco Cardin. On $C^0$-variational solutions for Hamilton-Jacobi equations. Discrete & Continuous Dynamical Systems - A, 2011, 31 (2) : 385-406. doi: 10.3934/dcds.2011.31.385 |
[11] |
Gawtum Namah, Mohammed Sbihi. A notion of extremal solutions for time periodic Hamilton-Jacobi equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 647-664. doi: 10.3934/dcdsb.2010.13.647 |
[12] |
Gui-Qiang Chen, Bo Su. Discontinuous solutions for Hamilton-Jacobi equations: Uniqueness and regularity. Discrete & Continuous Dynamical Systems - A, 2003, 9 (1) : 167-192. doi: 10.3934/dcds.2003.9.167 |
[13] |
David McCaffrey. A representational formula for variational solutions to Hamilton-Jacobi equations. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1205-1215. doi: 10.3934/cpaa.2012.11.1205 |
[14] |
Joan-Andreu Lázaro-Camí, Juan-Pablo Ortega. The stochastic Hamilton-Jacobi equation. Journal of Geometric Mechanics, 2009, 1 (3) : 295-315. doi: 10.3934/jgm.2009.1.295 |
[15] |
Eddaly Guerra, Héctor Sánchez-Morgado. Vanishing viscosity limits for space-time periodic Hamilton-Jacobi equations. Communications on Pure & Applied Analysis, 2014, 13 (1) : 331-346. doi: 10.3934/cpaa.2014.13.331 |
[16] |
Tomoki Ohsawa, Anthony M. Bloch. Nonholonomic Hamilton-Jacobi equation and integrability. Journal of Geometric Mechanics, 2009, 1 (4) : 461-481. doi: 10.3934/jgm.2009.1.461 |
[17] |
Claudio Marchi. On the convergence of singular perturbations of Hamilton-Jacobi equations. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1363-1377. doi: 10.3934/cpaa.2010.9.1363 |
[18] |
Isabeau Birindelli, J. Wigniolle. Homogenization of Hamilton-Jacobi equations in the Heisenberg group. Communications on Pure & Applied Analysis, 2003, 2 (4) : 461-479. doi: 10.3934/cpaa.2003.2.461 |
[19] |
María Barbero-Liñán, Manuel de León, David Martín de Diego, Juan C. Marrero, Miguel C. Muñoz-Lecanda. Kinematic reduction and the Hamilton-Jacobi equation. Journal of Geometric Mechanics, 2012, 4 (3) : 207-237. doi: 10.3934/jgm.2012.4.207 |
[20] |
Larry M. Bates, Francesco Fassò, Nicola Sansonetto. The Hamilton-Jacobi equation, integrability, and nonholonomic systems. Journal of Geometric Mechanics, 2014, 6 (4) : 441-449. doi: 10.3934/jgm.2014.6.441 |
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