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Commuting Hamiltonians and multi-time Hamilton-Jacobi equations

Franco Cardin·Claude Viterbo
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Abstract

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.

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Franco Cardin, Claude Viterbo. 2005-07-21. Commuting Hamiltonians and multi-time Hamilton-Jacobi equations. https://doi.org/10.1215/00127094-2008-036

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