Viscosity Solutions and Aubry-Mather theory
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منابع مشابه
Weak KAM Theory: the connection between Aubry-Mather theory and viscosity solutions of the Hamilton-Jacobi equation
The goal of this lecture is to explain to the general mathematical audience the connection that was discovered in the last 20 or so years between the Aubry-Mather theory of Lagrangian systems, due independently to Aubry and Mather in low dimension, and to Mather in higher dimension, and the theory of viscosity solutions of the Hamilton-Jacobi equation, due to Crandall and Lions, and more precis...
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The main objective of this paper is to prove new necessary conditions to the existence of KAM tori. These converse KAM conditions, can be used to detect gaps between KAM tori and Aubry-Mather sets. By exploring the connections between viscosity solutions of Hamilton-Jacobi equations, KAM and Aubry-Mather theories we develop a set of explicit a-priori estimates for smooth viscosity solutions tha...
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