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15 August 2008 Commuting Hamiltonians and Hamilton-Jacobi multi-time equations
Franco Cardin, Claude Viterbo
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Duke Math. J. 144(2): 235-284 (15 August 2008). DOI: 10.1215/00127094-2008-036

Abstract

The aim of this article is twofold. First, we show that the C0-limit of a pair of commuting Hamiltonians commutes. This means, on the one hand, that if the limit of the Hamiltonians is smooth, the Poisson bracket of their limit still vanishes and, on the other hand, that we may define “commutation” for C0-functions. The second part of this article deals with solving multi-time Hamilton-Jacobi equations using variational solutions. This extends the work of Barles and Tourin [BT] in the viscosity case to include the case of C0-Hamiltonians, and it removes their convexity assumption, provided that we work in the setting of variational solutions

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Franco Cardin. Claude Viterbo. "Commuting Hamiltonians and Hamilton-Jacobi multi-time equations." Duke Math. J. 144 (2) 235 - 284, 15 August 2008. https://doi.org/10.1215/00127094-2008-036

Information

Published: 15 August 2008
First available in Project Euclid: 14 August 2008

zbMATH: 1153.37029
MathSciNet: MR2437680
Digital Object Identifier: 10.1215/00127094-2008-036

Subjects:
Primary: 35F20, 57R17
Secondary: 35F25, 37J10, 49L25, 70H20

Rights: Copyright © 2008 Duke University Press

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Vol.144 • No. 2 • 15 August 2008
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