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Metric character of Hamilton-Jacobi equations

Author: Antonio Siconolfi
Journal: Trans. Amer. Math. Soc. 355 (2003), 1987-2009
MSC (2000): Primary 35F20, 49L25
Published electronically: January 8, 2003
Erratum: Trans. Amer. Math. Soc. (recently posted).
MathSciNet review: 1953535
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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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Additional Information

Antonio Siconolfi
Affiliation: Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro, 2, 00185 Roma, Italy

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
Published electronically: January 8, 2003
Additional Notes: Research partially supported by the TMR Network “Viscosity Solutions and Applications”
Article copyright: © Copyright 2003 American Mathematical Society