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

Olga Bernardi; Franco Cardin

doi:10.3934/cpaa.2006.5.793

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2006, Volume 5, Issue 4: 793-812. Doi: 10.3934/cpaa.2006.5.793

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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

Received: October 31, 2005

Revised: May 31, 2006

Published: November 2006

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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.

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Mathematics Subject Classification: Primary: 35A15, 35A30; Secondary: 53D35.

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