Existence of C 1 , 1 critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds

Patrick Bernard

Annales scientifiques de l'École Normale Supérieure (2007)

  • Volume: 40, Issue: 3, page 445-452
  • ISSN: 0012-9593

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Bernard, Patrick. "Existence of ${C}^{1,1}$ critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds." Annales scientifiques de l'École Normale Supérieure 40.3 (2007): 445-452. <http://eudml.org/doc/82717>.

@article{Bernard2007,
author = {Bernard, Patrick},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Mather theory; Aubry set},
language = {eng},
number = {3},
pages = {445-452},
publisher = {Elsevier},
title = {Existence of $\{C\}^\{1,1\}$ critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds},
url = {http://eudml.org/doc/82717},
volume = {40},
year = {2007},
}

TY - JOUR
AU - Bernard, Patrick
TI - Existence of ${C}^{1,1}$ critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2007
PB - Elsevier
VL - 40
IS - 3
SP - 445
EP - 452
LA - eng
KW - Mather theory; Aubry set
UR - http://eudml.org/doc/82717
ER -

References

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  1. [1] Bernard P., The dynamics of pseudographs in convex Hamiltonian systems, J. Am. Math. Soc., in press. Zbl1213.37089
  2. [2] Cannarsa P., Sinestrari C., Semiconcave Functions, Hamilton–Jacobi Equations and Optimal Control, Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser, 2004. Zbl1095.49003
  3. [3] Contreras G., Iturriaga R., Paternain G.P., Paternain M., Lagrangian graphs, minimizing measures and Mañé's critical values, Geom. Funct. Anal.8 (5) (1998) 788-809. Zbl0920.58015MR1650090
  4. [4] Fathi A., Weak KAM Theorem in Lagrangian Dynamics, book in press. 
  5. [5] Fathi A., Siconolfi A., Existence of C 1 critical sub-solutions of the Hamilton–Jacobi equation, Invent. Math.155 (2) (2004) 363-388. Zbl1061.58008
  6. [6] Fathi A., Siconolfi A., PDE aspects of Aubry–Mather theory for quasiconvex Hamiltonians, Calc. Var. Partial Differential Equations22 (2005) 185-228. Zbl1065.35092
  7. [7] Lasry J.M., Lions J.L., A remark on regularization in Hilbert spaces, Israel J. Math.55 (3) (1986) 257-266. Zbl0631.49018MR876394
  8. [8] Massart D., Sub-solutions of time-periodic Hamilton–Jacobi equations, Ergodic Theory Dynam. Systems, in press. Zbl1121.37049

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