Global subanalytic solutions of Hamilton-Jacobi type equations

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 23, Issue 3, 2006, Pages 363-387

  Trélat, Emmanuel ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Hamilton Jacobi equation; Subanalytic sets; Value function; Viscosity solution

Indexed keywords

COMPUTATIONAL GEOMETRY; FUNCTIONS; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING; VISCOSITY;

HAMILTON-JACOBI EQUATION; SUBANALYTIC SETS; VALUE FUNCTION; VISCOSITY SOLUTION;

HAMILTONIANS;

EID: 33645410758     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2005.05.002     Document Type: Article

References (36)

1. A. Agrachev Compactness for sub-Riemannian length minimizers and subanalyticity Rend. Sem. Mat. Torino 56 1999
2. A. Agrachev, B. Bonnard, M. Chyba, and I. Kupka Sub-Riemannian sphere in the Martinet flat case ESAIM Control Optim. Calc. Var. 2 1997 377 448
3. A. Agrachev, and J.P. Gauthier On subanalyticity of Carnot- Carathéodory distances Ann. Inst. H. Poincaré Anal. Non Linéaire 18 2001 3
4. A. Agrachev, and A. Sarychev Sub-Riemannian metrics: minimality of singular geodesics versus subanalyticity ESAIM Control Optim. Calc. Var. 4 1999 377 403
5. P. Albano, and P. Cannarsa Structural properties of singularities of semiconcave functions Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 4 1999 719 740
6. G. Alberti, L. Ambrosio, and P. Cannarsa On the singularities of convex functions Manuscripta Math. 76 3-4 1992 421 435
7. F. Alouges, S. Labbé. Z-invariant micromagnetic configurations, Preprint Univ. Paris Sud, Orsay, 2005
8. L. Ambrosio, P. Cannarsa, and H.M. Soner On the propagation of singularities of semi-convex functions Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 20 4 1993 597 616
9. M. Bardi, and I. Capuzzo-Dolcetta Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations 1997 Birkhäuser Boston
10. G. Barles Solutions de viscosité des équations de Hamilton-Jacobi Math. Appl. vol. 17 1994 Springer-Verlag
11. A. Bellaïche Tangent space in sub-Riemannian geometry Sub-Riemannian Geometry 1996 Birkhäuser
12. B. Bonnard, and M. Chyba Singular trajectories and their role in control theory Math. Appl. 40 2003
13. B. Bonnard, and E. Trélat On the role of singular minimizers in sub-Riemannian geometry Ann. Fac. Sci. Toulouse (6) X 3 2001 405 491
14. P. Cannarsa, A. Mennucci, and C. Sinestrari Regularity results for solutions of a class of Hamilton-Jacobi equations Arch. Rational Mech. Anal. 40 1997 197 223
15. P. Cannarsa, and C. Sinestrari Convexity properties of the minimum time function Calc. Var. Partial Differential Equations 3 1995 273 298
16. P. Cannarsa, and C. Sinestrari Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control Progr. Nonlinear Differential Equations Appl. vol. 58 2004 Birkhäuser Boston
17. P. Cannarsa, and H.M. Soner On the singularities of the viscosity solutions to Hamilton-Jacobi-Bellman equations Indiana Univ. Math. J. 36 3 1987 501 524
18. Y. Chitour, F. Jean, and E. Trélat Propriétés génériques des trajectoires singulières C. R. Acad. Sci. Paris, Ser. I 337 1 2003 49 52
19. Y. Chitour, F. Jean, E. Trélat. Genericity properties for singular trajectories, J. Differential Geom. (2005), in press
20. M.G. Crandall, and P.-L. Lions Viscosity solutions of Hamilton-Jacobi equations Trans. Amer. Math. Soc. 277 1983 1 42
21. L.C. Evans Partial Differential Equations 1998 Amer. Math. Soc.
22. A. Fathi Weak KAM Theorem and Lagrangian Dynamics 2003 Cambridge University Press
23. R.M. Hardt Stratification of real analytic mappings and images Invent. Math. 28 1975
24. H. Hironaka Subanalytic sets Number Theory, Algebraic Geometry and Commutative Algebra. In honor of Y. Akizuki, Tokyo 1973
25. H. Ishii On representation of solutions of Hamilton-Jacobi equations with convex Hamiltonians Lecture Notes Numer. Appl. Anal. vol. 8 1985 15 22
26. V. Jurdjevic Geometric Control Theory 1997 Cambridge University Press
27. P.-L. Lions Generalized Solutions of Hamilton-Jacobi Equations 1982 Pitman
28. L.S. Pontryagin, V.G. Boltyanskij, R.V. Gamkrelidze, and E.F. Mishchenko The Mathematical Theory of Optimal Processes 1962 Interscience Publishers, John Wiley & Sons New York
29. F. Rampazzo, Faithful representations for convex Hamilton-Jacobi equations, Preprint, Univ. di Padova
30. L. Rifford Semiconcave control-Lyapunov functions and stabilizing feedbacks SIAM J. Control Optim. 41 3 2002 659 681
31. L. Rifford Singularities of viscosity solutions and the stabilization problem in the plane Indiana Univ. Math. J. 52 5 2003 1373 1396
32. M. Tamm Subanalytic sets in the calculus of variations Acta Math. 146 1981
33. E. Trélat Some properties of the value function and its level sets for affine control systems with quadratic cost J. Dynam. Control Systems 6 4 2000 511 541
34. E. Trélat, Etude asymptotique et transcendance de la fonction valeur en contrôle optimal; catégorie log-exp en géométrie sous-Riemannienne dans le cas Martinet, Thèse, Univ. de Bourgogne, 2000
35. E. Trélat Solutions sous-analytiques globales de certaines équations d'Hamilton-Jacobi C. R. Acad. Sci. Paris, Ser. I 337 10 2003 653 656
36. L. van den Dries, and C. Miller Geometric categories and o-minimal structures Duke Math. J. 84 2 1996