Transactions of the American Mathematical Society

Author(s): Antonio Siconolfi
Journal: Trans. Amer. Math. Soc. 355 (2003), 1987-2009.
MSC (2000): Primary 35F20, 49L25
Posted: January 8, 2003
Errata: Trans. Amer. Math. Soc. (recently posted).
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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.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35F20, 49L25

Antonio Siconolfi
Affiliation: Dipartimento di Matematica, Università di Roma ``La Sapienza'', Piazzale Aldo Moro, 2, 00185 Roma, Italy
Email: siconolfi@mat.uniroma1.it

DOI: 10.1090/S0002-9947-03-03237-9
PII: S 0002-9947(03)03237-9
Keywords: Hamilton--Jacobi equations, viscosity solutions, distance functions
Received by editor(s): May 9, 2000
Received by editor(s) in revised form: May 18, 2001
Posted: January 8, 2003
Additional Notes: Research partially supported by the TMR Network ``Viscosity Solutions and Applications''
Copyright of article: Copyright 2003, American Mathematical Society

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