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December  2006, 5(4): 793-812. doi: 10.3934/cpaa.2006.5.793

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

Olga Bernardi 1, and  Franco Cardin 1,

1. 

Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7 - 35131 Padova, Italy, Italy

Received  November 2005 Revised  June 2006 Published  September 2006

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: symplectic topology, Hamilton-Jacobi theory, viscosity solutions..
Mathematics Subject Classification: Primary: 35A15, 35A30; Secondary: 53D3.
Citation: Olga Bernardi, Franco Cardin. Minimax and viscosity solutions of Hamilton-Jacobi equations in the convex case. Communications on Pure and Applied Analysis, 2006, 5 (4) : 793-812. doi: 10.3934/cpaa.2006.5.793
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