Commuting Hamiltonians and multi-time Hamilton-Jacobi equations

Details Commuting Hamiltonians and multi-time Hamilton-Jacobi equations Commuting Hamiltonians and multi-time Hamilton-Jacobi equations

2005-07-21

arxiv.org/abs/math/0507418v2

Duke Mathematical Journal 144, 2 (2008) 235-284

Mathematics

Symplectic Geometry

Scientific paper

10.1215/00127094-2008-036

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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