M. Bardi and I. Capuzzo-dolcetta, Optimal Control and Viscosity Solutions of Hamilton- Jacobi-Bellman Equations, 1997.
DOI : 10.1007/978-0-8176-4755-1

G. Barles, Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: a guided visit, Nonlinear Analysis: Theory, Methods & Applications, vol.20, issue.9, pp.1123-1134, 1993.
DOI : 10.1016/0362-546X(93)90098-D

G. Barles and P. E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, 29th IEEE Conference on Decision and Control, pp.271-283, 1991.
DOI : 10.1109/CDC.1990.204046

E. N. Barron and R. Jensen, Semicontinuous Viscosity Solutions For Hamilton???Jacobi Equations With Convex Hamiltonians, Communications in Partial Differential Equations, vol.10, issue.12, pp.15-1713, 1990.
DOI : 10.1007/BF02765025

O. Bokanowski, N. Forcadel, and H. Zidani, $L^1$-error estimates for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1, Mathematics of Computation, vol.79, issue.271, pp.1395-1426, 2010.
DOI : 10.1090/S0025-5718-10-02311-2

M. G. Crandall and P. L. Lions, Two approximations of solutions of Hamilton-Jacobi equations, Mathematics of Computation, vol.43, issue.167, pp.1-19, 1984.
DOI : 10.1090/S0025-5718-1984-0744921-8

E. Cristiani and M. Falcone, Fast Semi-Lagrangian Schemes for the Eikonal Equation and Applications, SIAM Journal on Numerical Analysis, vol.45, issue.5, pp.1979-2011, 2007.
DOI : 10.1137/050637625

K. P. Deckelnick and C. M. Elliott, Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities, Interface. free bound, pp.329-349, 2004.
DOI : 10.4171/ifb/103

M. Falcone and R. Ferretti, Semi-Lagrangian Schemes for Hamilton???Jacobi Equations, Discrete Representation Formulae and Godunov Methods, Journal of Computational Physics, vol.175, issue.2, pp.559-575, 2002.
DOI : 10.1006/jcph.2001.6954

M. Falcone and R. Ferretti, Semi?Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations, SIAM, 2013.
DOI : 10.1137/1.9781611973051

URL : https://hal.archives-ouvertes.fr/hal-00916055

H. Frankowska, Lower Semicontinuous Solutions of Hamilton???Jacobi???Bellman Equations, SIAM Journal on Control and Optimization, vol.31, issue.1, pp.257-272, 1993.
DOI : 10.1137/0331016

A. Festa and M. Falcone, An Approximation Scheme for an Eikonal Equation with Discontinuous Coefficient, SIAM Journal on Numerical Analysis, vol.52, issue.1
DOI : 10.1137/120901829

URL : https://hal.archives-ouvertes.fr/hal-01067426

H. Ishii, Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets, Bull. Fac. Sci. Engrg. Chuo Univ, vol.28, pp.33-77, 1985.

H. Ishii, A simple, direct proof of uniqueness for solutions of the Hamilton-Jacobi equations of eikonal type, Proc. Amer, pp.247-251, 1987.
DOI : 10.1090/S0002-9939-1987-0884461-3

C. T. Lin and E. Tadmor, $L^1$-Stability and error estimates for approximate Hamilton-Jacobi solutions, Numerische Mathematik, vol.87, issue.4, pp.701-735, 2001.
DOI : 10.1007/PL00005430

R. T. Newcomb and J. Su, Eikonal equations with discontinuities, Diff. Integral Equations, vol.8, pp.1947-1960, 1995.

P. Soravia, Degenerate Eikonal equations with discontinuous refraction index, ESAIM: Control, Optimisation and Calculus of Variations, vol.12, issue.2, pp.216-230, 2006.
DOI : 10.1051/cocv:2005033

E. Tadmor, Local Error Estimates for Discontinuous Solutions of Nonlinear Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.28, issue.4, pp.891-904, 1991.
DOI : 10.1137/0728048

A. Turin, A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems, Numerische Mathematik, vol.59, issue.2, pp.75-85, 1992.
DOI : 10.1007/BF01396221