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

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.

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Bibliographic Details
Published inProceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 142; no. 6; pp. 1193 - 1236
Main Author Fathi, Albert
Format Journal Article
LanguageEnglish
Published Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.12.2012
Cambridge University Press
Subjects
Hamilton-Jacobi equation
Manifolds
Partial differential equations
Topological manifolds
Viscosity
Online AccessGet full text
ISSN0308-2105
1473-7124
DOI10.1017/S0308210550000064

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Summary: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.
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ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210550000064