Minimax and viscosity solutions of Hamilton-Jacobi equations in the convex case

Pages: 793 - 812, Volume 5, Issue 4, December 2006

doi:10.3934/cpaa.2006.5.793       Abstract        Full Text (219.8K)       Related Articles

Olga Bernardi - Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7 - 35131 Padova, Italy (email)
Franco Cardin - 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.
Mathematics Subject Classification:  Primary: 35A15, 35A30; Secondary: 53D35.

Received: November 2005;      Revised: June 2006;      Published: September 2006.