Minimax and viscosity solutions of Hamilton-Jacobi equations in the convex case
Olga Bernardi - Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7 - 35131 Padova, Italy (email)
Abstract: The aim of this paper is twofold. We construct an extension to a non-integrable case of Hopf's formula, often used to produce viscosity solutions of Hamilton-Jacobi equations for $p$-convex integrable Hamiltonians. Furthermore, for a general class of $p$-convex Hamiltonians, we present a proof of the equivalence of the minimax solution with the viscosity solution.
Keywords: Hamilton-Jacobi theory, symplectic topology, viscosity solutions.
Received: November 2005; Revised: June 2006; Published: September 2006.
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