Weak KAM from a PDE point of view: viscosity solutions of the Hamilton–Jacobi equation and Aubry set

Albert Fathi

doi:10.1017/S0308210550000064

Abstract

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We introduce the notion of a viscosity solution for the first-order Hamilton–Jacobi equation, in the more general setting of manifolds, to obtain a weak KAM theory using only tools from partial differential equations. This work should be accessible to people with no prior knowledge of the subject.

Crossref Citations

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Weak KAM from a PDE point of view: viscosity solutions of the Hamilton–Jacobi equation and Aubry set

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