Commuting Hamiltonians and multi-time Hamilton-Jacobi equations

Franco Cardin (1) , Claude Viterbo (2)

1 Dipartimento di Matematica Pura e Applicata [Padova]
2 CMLS - Centre de Mathématiques Laurent Schwartz

We prove that if a sequence of pairs of smooth commuting Hamiltonians converge in the $C^0$ topology to a pair of smooth Hamiltonians, these commute. This allows us define the notion of commuting continuous Hamiltonians. As an application we extend some results of Barles and Tourin on multi-time Hamilton-Jacobi equations to a more general setting.

Mots clés: Hamiltonians; Poisson commutation; Hamilton-Jacobi equations; variational solutions

Domaines: Géométrie symplectique [math.SG]; Equations aux dérivées partielles [math.AP]

Franco Cardin, Claude Viterbo. Commuting Hamiltonians and multi-time Hamilton-Jacobi equations. Duke Mathematical Journal, 2008, 144 (2), pp.235-284. ⟨10.1215/00127094-2008-036⟩. ⟨hal-00007603v2⟩