An Hopf-Lax formula for a class of measurable Hamilton-Jacobi equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 57, Issue 2, 2004, Pages 265-286

  Camilli, Fabio ^a  

^a UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

Approximation; Hopf Lax formulas; Measurable Hamilton Jacobi equations; Viscosity solutions

Indexed keywords

APPROXIMATION THEORY; CURVE FITTING; HAMILTONIANS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; VISCOSITY;

HOPF-LAX FORMULAS; MEASURABLE HAMILTON-JACOBI EQUATIONS; VISCOSITY SOLUTIONS;

NONLINEAR EQUATIONS;

EID: 2342466049     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.02.013     Document Type: Article

References (23)

1. Bardi M., Capuzzo Dolcetta I. Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. 1997;Birkhäuser, Boston.
2. Bardi M., Falcone M. An approximation scheme for the minimum time function. SIAM J. Control Optim. 28:1990;950-965.
3. M. Bardi, M. Falcone, Discrete approximation of the minimal time function for system with regular optimal trajectories, Analysis and Optimization of Systems, Antibes, 1990, Lecture Notes in Control and Information Sciences, Vol. 144, Springer, Berlin, 1990, pp. 103-112.
4. G. Barles, Remark on a flame propagation model, Report INRIA (1985) #464.
5. Barles G., Roquejoffre J.M. Large time behaviour of fronts governed by eikonal equations. Interfaces Free Bound. 5:2003;83-102.
6. Barles G., Soner H.M., Souganidis T. Front propagations and phase field theory. SIAM J. Control Optim. 31:1993;439-469.
7. Caffarelli L., Crandall M.C., Kocan M., Swiech A. On viscosity solutions of fully nonlinear equations with measurable ingredients. Comm. Pure Appl. Math. 49:1996;365-397.
8. Camilli F., Grüne L. Numerical approximation of the maximal solution for a class of degenerate Hamilton-Jacobi equations. SIAM J. Numer. Anal. 38:2000;1540-1560.
9. Camilli F., Siconolfi A. Discontinuous solutions of an Hamilton-Jacobi equation with infinite speed of propagation. SIAM J. Math. Anal. 28:1997;1421-1447.
10. Camilli F., Siconolfi A. Hamilton-Jacobi equations with measurable dependence on the state variable. Adv. Differential Equations. 8:2003;733-768.
11. I. Capuzzo Dolcetta, The Hopf solution of Hamilton-Jacobi equations, in: Elliptic and Parabolic Problems, Rolduc/Gaeta, 2001, World Scientific Publishing, River Edge, NJ, 2002, pp. 343-351.
12. De Cecco G., Palmieri G. LIP manifolds. from metric to Finslerian structure Math. Z. 218:1995;223-237.
13. Falcone M., Giorgi T., Loreti P. Level sets of viscosity solutions. some applications to fronts and rendezvous problems SIAM J. Appl. Math. 54:1994;1335-1354.
14. Y. Giga, Surface evolution equations - a level set method, Hokkaido Univ. Technical Report Series in Mathematics #71, 2002.
15. Lions P.L. Generalized Solutions of Hamilton-Jacobi Equations. 1982;Pitman, London.
16. Newcomb II R.T., Su J. Eikonal equations with discontinuities. Differential Integral Equations. 8(8):1995;1947-1960.
17. Ostrov D. Solutions of Hamilton-Jacobi equations and scalar conservation laws with discontinuous space-time dependance. J. Differential Equations. 182:2002;51-77.
18. Siconolfi A. A first order Hamilton-Jacobi equation with singularity and the evolution of level sets. Comm. Partial Differential Equations. 20:1995;277-308.
19. A. Siconolfi, Representation formulae and comparison results for geometric Hamilton-Jacobi equations, preprint, 2001.
20. Soravia P. Generalized motion of front along its normal direction. a differential game approach Nonlinear Anal. TMA. 22:1994;1247-1262.
21. Soravia P. Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian. Indiana Univ. Math. J. 51:2002;451-477.
22. Sethian J. Curvature and the evolution of fronts. Comm. Math. Phys. 101:1985;487-499.
23. Ziemer W. Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation. Graduate Texts in Mathematics. Vol. 120:1989;Springer, New York.