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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| Published in | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 142; no. 6; pp. 1193 - 1236 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Edinburgh, UK
Royal Society of Edinburgh Scotland Foundation
01.12.2012
Cambridge University Press |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0308-2105 1473-7124 |
| DOI | 10.1017/S0308210550000064 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. [PUBLICATION ABSTRACT] 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. |
| Author | Fathi, Albert |
| Author_xml | – sequence: 1 givenname: Albert surname: Fathi fullname: Fathi, Albert email: albert.fathi@ens-lyon.fr organization: Unité de Mathématiques Pures et Appliquées, École Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon cedex 07, Francealbert.fathi@ens-lyon.fr) |
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| Copyright | Copyright © Royal Society of Edinburgh 2012 |
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| DOI | 10.1017/S0308210550000064 |
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| Snippet | 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... 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... |
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| SubjectTerms | Hamilton-Jacobi equation Manifolds Partial differential equations Topological manifolds Viscosity |
| Title | Weak KAM from a PDE point of view: viscosity solutions of the Hamilton–Jacobi equation and Aubry set |
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