G. Barles, A. Briani, and A. E. Chasseigne, A Bellman approach for two-domains optimal control problems in R N , ESAIM:COCV, accepted for publication, 2012.

M. Bardi and A. , Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Systems and Control: Foundations and Applications, 1997.

A. Briani and A. A. Davini, Monge solutions for discontinuous Hamiltonians, ESAIM. Control, Optimisation and Calculus of Variations, pp.229-251, 2005.

A. Bressan and A. Y. Hong, Optimal control problems for control systems on stratified domains, Network and Heterogeneous Media, pp.313-331, 2007.

R. C. Barnard and A. P. Wolenski, Flow invariance on stratified domains, submitted, preprint available on arXiv, 2012.

F. H. Clarke, Optimization and Nonsmooth Analysis, Society for Industrial Mathematics, 1990.
DOI : 10.1137/1.9781611971309

F. H. Clarke, Y. S. Ledyaev, R. J. Stern, and A. P. Wolenski, Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics, vol.178
URL : https://hal.archives-ouvertes.fr/hal-00863298

F. Camilli and A. A. Siconolfi, Hamilton-Jacobi equations with measurable dependence on the state variable Advances in Differential Equations, pp.733-768, 2003.

G. Dal-maso and A. H. Frankowska, Value functions for Bolza problems with discontinuous Lagrangians and Hamilton-Jacobi inequalities, ESAIM: Control, Optimisation and Calculus of Variations, vol.5, pp.369-394
DOI : 10.1051/cocv:2000114

A. F. Filippov, Differential equations with discontinuous right-hand side, 1988.
DOI : 10.1090/trans2/042/13

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

H. Ishii, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations, Ann. Sc. Norm. Sup. Pisa (IV), vol.16, pp.105-135, 1989.

C. Imbert, R. Monneau, A. H. Zidani, and . Hamilton, A Hamilton-Jacobi approach to junction problems and application to traffic flows, ESAIM: Control, Optimisation and Calculus of Variations, vol.19, issue.1, 2012.
DOI : 10.1051/cocv/2012002

URL : https://hal.archives-ouvertes.fr/hal-00569010

Z. Rao, A. Siconolfi, and A. H. Zidani, Stationary Hamilton-Jacobi-Bellman equations on multi-domains, preprint in preparation

P. Soravia, Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian, Indiana University Mathematics Journal, vol.51, issue.2, pp.451-477, 2002.
DOI : 10.1512/iumj.2002.51.2105