On vectorial Hamilton-Jacobi equations

Cyril Imbert (1) , Michel Volle (2)

1 MIP - Mathématiques pour l'Industrie et la Physique
2 LANLG - Laboratoire d'Analyse non linéaire et Géométrie

We consider the generalized Hopf and Lax functions associated with a vector-valued hamiltonian and we prove that they still provide lower semicontinuous solutions for the corresponding vectorial Hamilton-Jacobi equation in a very general context. Uniqueness of these generalized solutions is also investigated.

Mots clés: Hamilton-Jacobi equations; vector-valued Hamiltonian; Hopf-Lax formulae

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert, Michel Volle. On vectorial Hamilton-Jacobi equations. Control and Cybernetics, 2002, 31 (3), pp.493-506. ⟨hal-00176540⟩