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. Further- more, for a general class of p-convex Hamiltonians, we present a proof of the equivalence of the minimax solution with the viscosity solution.
Minimax and viscosity solutions of Hamilton-Jacobi equations in the convex case.
BERNARDI, OLGA;CARDIN, FRANCO
2006
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. Further- more, for a general class of p-convex Hamiltonians, we present a proof of the equivalence of the minimax solution with the viscosity solution.File in questo prodotto:
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