Metric character of Hamilton–Jacobi equations

Siconolfi, Antonio

doi:10.1090/S0002-9947-03-03237-9

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.

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