Commuting Hamiltonians and Hamilton-Jacobi multi-time equations
By Franco Cardin, C. Viterbo. 2005
84 citations recorded by the source corpus.
The aim of this paper is twofold: first of all, we show that the C 0 limit of a pair of commuting Hamiltonians commute. This means on 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 C 0 functions. The second part of the paper deals with solving "multi-time" Hamilton- Jacobi equations using variational solutions. This extends the work of Barles and Tourin in the viscosity case to include the case of C 0 Hamiltonians, and removes their convexity assumption, provided we are in the framework of "variational solutions".
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5b0101b1f936556025e77b272baaceae13ff113f
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In Applied Mathematics
- F. Zapolsky
- Michael Entov
- Guy Barles
- L. Polterovich
- Russell W. Schwab
- Luis Silvestre
- Adina Ciomaga
- Xavier Ros-Oton
In Geometry and Topology
- F. Zapolsky
- Michael Entov
- L. Polterovich
- Guy Barles
- Michael Usher
- Yong-Geun Oh
- E. Shelukhin
- V. Ginzburg
In Mathematical Physics
- F. Zapolsky
- Michael Entov
- L. Polterovich
- Guy Barles
- Michael Usher
- Yong-Geun Oh
- E. Shelukhin
- Y. Ostrover
Citations in the corpus
- An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications (2013, methodology): “For such properties of commutations of semi-groups, we refer the reader to Cardin and Viterbo [20], Motta and Rampazzo [41] and Tourin and the author [16].”
- Symplectic quasi-states and semi-simplicity of quantum homology (2007, background): “[ 7 ]: while the definition of the Poisson brackets {F, G} involves the first derivatives of F and G, it turns out that when the function {F, G} is not identically zero its C0-norm cannot be made arbitrarily small by arbitrarily C0-small perturbations of F and G. Symplectic quasi-states can be used ”
- Quasi-morphisms and the Poisson bracket (2006, background): “The same holds true for ˆtF and ˆsG with any s;t 2 R and hence fF;Gg · 0. This proves implication (6) which appears in [ 4 ].”