Minimax and viscosity solutions of Hamilton-Jacobi equations in the convex case
Olga Bernardi, Franco Cardin · Communications on Pure & Applied Analysis · 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.