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Article Contents

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

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

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