Metric character of Hamilton–Jacobi equations
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- by Antonio Siconolfi PDF
- Trans. Amer. Math. Soc. 355 (2003), 1987-2009 Request permission
Erratum: Trans. Amer. Math. Soc. 355 (2003), 4265-4265.
Abstract:
We deal with the metrics related to Hamilton–Jacobi equations of eikonal type. If no convexity conditions are assumed on the Hamiltonian, these metrics are expressed by an $\inf$–$\sup$ formula involving certain level sets of the Hamiltonian. In the case where these level sets are star–shaped with respect to 0, we study the induced length metric and show that it coincides with the Finsler metric related to a suitable convexification of the equation.References
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Additional Information
- Antonio Siconolfi
- Affiliation: Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro, 2, 00185 Roma, Italy
- Email: siconolfi@mat.uniroma1.it
- Received by editor(s): May 9, 2000
- Received by editor(s) in revised form: May 18, 2001
- Published electronically: January 8, 2003
- Additional Notes: Research partially supported by the TMR Network “Viscosity Solutions and Applications”
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 1987-2009
- MSC (2000): Primary 35F20, 49L25
- DOI: https://doi.org/10.1090/S0002-9947-03-03237-9
- MathSciNet review: 1953535